Questions on Geometry: Polygons answered by real tutors!

Tutors Answer Your Questions about Polygons (FREE)

Question 571345: How do i prove all the angles of a pentagon are congruent if i know that there are five congruent sides and 3 congruent angles?
Answer by Edwin McCravy(6932)

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There are two cases.  One case is when the three angles that are given
congruent are adjacent (the first figure below), and the other case is 
when they are not (the second figure below.   Mostly I will give only
the steps.  You must give the reasons.   
 


Case 1:

Given: AB ≅ BC ≅ CD ≅ DE ≅ EA
       ∠A ≅ ∠B ≅ ∠E  
        


 1. Draw BE, BD and EC
 2. AB ≅ BE                      (Given)
 3. ᐃABE is isosceles
 4. ∠ABE ≅ ∠AEB
 5. ∠ABC ≅ ∠AED                      (Given) 
 6. m∠ABC - m∠ABE = m∠AED - m∠AEB
 7. ∠CBE ≅ ∠DEB
 8. BE ≅ BE
 9. BC ≅ ED                          (Given)
10. ᐃBCE ≅ ᐃEDB                      SAS
11. BD ≅ EC
12. BC ≅ ED                          (Given)
13. CD ≅ CD
14. ᐃBCD ≅ ᐃEDC                     SSS 
15. ∠BCD ≅ ∠EDC

-------------------------------
Case 2.

Given: AB ≅ BC ≅ CD ≅ DE ≅ EA
       ∠A ≅ ∠C ≅ ∠D 



 1. Draw BE, BD and EC
 2. ∠BCD ≅ ∠EDC               given
 3. BC ≅ DE                   given 
 4. CD ≅ CD                
 5. ᐃBCD ≅ ᐃEDC               SAS
 6. BD ≅ EC
 7. BC ≅ DE                   given
 8. BE ≅ BE
 9. ᐃBCE ≅ ᐃEDB
10. AB ≅ AE                   given
11. ᐃABE is isosceles
12. ∠ABE ≅ ∠AEB
13. ∠DBE ≅ ∠BEC
14. ∠CBD ≅ ∠DEC
15. m∠ABE + m∠DBE + m∠CBD = m∠AEB + m∠BEC + m∠DEC
16. ∠ABC ≅ ∠AED

Edwin

Question 571070: What is the height and radius of a cube with a volume of 113.1, with an answer in centimeters preferably??
Thank you, I apreciate your help

Answer by rfer(10417)

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A cube does not have a radius.
Each side is cu rt 113.1=4.836 cm

Question 571027: how do you find the area of a 20-ogon
Answer by Alan3354(21555)

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If you're given the side length, the apothem, or the radius, you use the formula for that.
If you're given the coordinates of the vertices, it's a different method.

Question 570408: If the exterior angle of a regular polyogn is 15, how do you find the central angle?
Answer by Alan3354(21555)

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If the exterior angle of a regular polyogn is 15, how do you find the central angle?
------------
They're equal

Question 570360: if a polygon is regular and one of the vertex angles is 165 degrees, how many sides must it have?
Answer by Alan3354(21555)

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if a polygon is regular and one of the vertex angles is 165 degrees, how many sides must it have?
------------
Exterior angles = 180 - 165 = 15 degs
360/15 = 24 sides

Question 570021: If you were to place a rhombus in the coordinate plane so that its diagonals lie along the axes, what would be the coordinates of the vertices using as few variables as possible?
Answer by solver91311(12118)

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Rhombus diagonals bisect each other, so if the diagonals lie on the axes, then the opposite vertices (the endpoints of the diagonals) are equidistant from the origin. Further, the vertices must lie on the axes as well, so you only need two variables for the 4 vertices.

John

My calculator said it, I believe it, that settles it

The Out Campaign: Scarlet Letter of Atheism

Question 569498: Hi,
1. suppose that the sum of the measures of the vertex angles of a polygon is 1620 degrees. How many sides does the polygon have?
what I've tried:
(n-2)180/n= i multiplied "n" by both sides to cancel out the fraction and then use distribution property to fix the equation.
180n - 360= 1620n
-180n 180n
-360= 1440n
-0.25=n
but that is the wrong answer. the book says that the answer of sides is 11.
Please help me.

Answer by KMST(578)

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I know your frustration. It's hard to figure out one's own mistake, and it is obvious that a polygon could not have -0.25 sides.
%28n-2%29180%2Fn

would be the measure of one angle in a regular n-sided polygon. That's probably what you were thinking of, but the problem refers to the sum of the measures of the angles.
The sum of the measures of the vertex angles of an n-sided polygon is %28n-2%29180

.
If

-->

-->

-->

-->

Question 568980: what is the perimeter of a regular dodecagon (a polygon which has 12 sides)whose area is 24 + 12 sqrt(3).
Answer by KMST(578)

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To calculate the area of regular polygon with N sides, the polygon can be sliced pizza-style into N isosceles triangles with one side as the base, and the area of those triangles can be calculated.
The height of those triangles is called the apothem, and can be calculated based on the length of the side, s, and half of the vertex angle, which depends on the number of sides, N.
drawing%28300%2C160%2C-2%2C28%2C-8%2C8%2C%0D%0Atriangle%280%2C7%2C0%2C-7%2C26.124%2C0%29%2C%0D%0Aline%280%2C0%2C26.124%2C0%29%2C%0D%0Alocate%288%2C0%2Capothem%29%2C+locate%28-1.2%2C1.1%2Cs%29%2Clocate%2820%2C1.5%2CB%29%2C%0D%0Aarrow%28-1%2C0.8%2C-1%2C7%29%2Carrow%28-1%2C-0.8%2C-1%2C-7%29%0D%0A%29

drawing%28300%2C160%2C-2%2C28%2C-8%2C8%2C%0D%0Atriangle%280%2C7%2C0%2C-7%2C26.124%2C0%29%2C%0D%0Aline%280%2C0%2C26.124%2C0%29%2C%0D%0Alocate%288%2C0%2Capothem%29%2C+locate%28-1.2%2C1.1%2Cs%29%2Clocate%2820%2C1.5%2CB%29%2C%0D%0Aarrow%28-1%2C0.8%2C-1%2C7%29%2Carrow%28-1%2C-0.8%2C-1%2C-7%29%0D%0A%29

For a dodecagon, the half of the vertex angle is B=360%5Eo%2F24

Putting it all together, the area,

, of a regular polygon with

sides of length

if you prefer your angles in degrees.
With N=12

A=s%5E2%2A12%2F%284tan%28180%5Eo%2F12%29%29=3s%5E2%2Ftan%2815%5Eo%29

-->

-->

as can be calculated from tan%2845%5Eo%29

and

using the formula (trigonometric identity) for tangent of a difference.
So s%5E2=Atan%2815%5Eo%29%2F3

with

A=24%2B12sqrt%283%29=12%282%2Bsqrt%283%29%29

and

gives us

s%5E2=12%282%2Bsqrt%283%29%29%282-sqrt%283%29%29%2F3=12%282%5E2-%28sqrt%283%29%29%5E2%29%2F3=4%284-3%29=4%2A1=4

The length of a side of the polygon is s=2

and the perimeter is 12%2A2=highlight%2824%29

Question 569384: Please help!!!! I will praise you!!!
At 9:30 am tomorrow, we open our doors for the last time. The price of every item in the store will be reduced 10% every hour, on the hour, beginning at 10am until everything goes, The stereo calvin would love to buy is $359 dollars.. Calvin has saved $270 for the stereo. Henry told calvin that at 11:01 am, the price of the stereo will be $287.20. Jacob says $290.79 will be the price. What might he expect the price to be at 11:01 and why? Henry claims that since the prices go down 105 every hour, after 10 hours, the stereo will be free. He tells calvin to arrive at the store at 8pm for a free stereo. Do you agree with Henry's reasoning? Explain why and why not. Sales tax is 6%. Assuming he gets no more money, explain to Calvin when he will be able to afford the stereo and how you figured this out. Be sure your work is shown in an organized format so that it can be easily followed

THANKS SOO MUCH!!!!!!!!!!!!!!!!! :DDDDDDDDDDDDDDDD
Found 2 solutions by solver91311, IWork4Dessert:
Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

The total amount to be paid after the first 10% reduction (considering the 6% sales tax) is:

The second hour

or

and, in general, after hours:

Since Calvin's funds are limited to $270.00, we need to solve

for and round up to the next higher integer.

Take the natural log of both sides

Use

to write

then

Round up

So the total amount will be less than Calvin's $270 right after the fourth hour. 10 is the first hour, 11 is the second hour...

So Calvin needs to come in at 1:00 pm when the total amount will be:

Which means that Calvin can go to lunch as long as he doesn't spend more than for his meal including tax and tip.

The only flaw in Calvin's plan is: What if there are a limited number of these stereo sets -- a number less than or equal to the number of people who come in at noon with $280 in their pocket? In such an event, Calvin is out of luck.

And by the way, Henry is an idiot. You take 10% off the CURRENT price, not the FULL price, each hour.

Super Double Plus Extra Credit

Theoretically, the price will never reach zero since after any reduction, 90 percent of the previous amount remains. However, a point will be reached eventually such that the total amount, including tax, will be reduced to an amount when rounded to the nearest one cent will be $0.00. Using the process outlined above, how many hours must elapse before he would actually receive the item absolutely free? Hint: What value of t makes the total price less than $0.005?

John

My calculator said it, I believe it, that settles it

Answer by IWork4Dessert(57)   (Show Source):
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Wow, what a mouthful!
Let's break this into more reasonable chunks. First of all, you know that you have a $359 stereo and only $270 to buy it with. At 10 AM, the stereo will be only $323.10(divide $359 by 10 and subtract that number from $359). At 11 AM, the stereo will be $290.79.
The reasoning: To find the price after a 10% discount, you need to find 10% of the number and then subtract it from the number.
At 12 PM, the stereo will be $261.72. At this point, Calvin can afford it, but keep in mind that there's 6% sales tax. To find 6% of $261.72, set up a proportion:
6/100=x/261.72.
Keep in mind that 6% is just 6 out of 100, which will be proportional to an amount out of the price. Cross-multiply to get x alone. Then divide both sides by 100 so that x is equal to 15.7. Add $15.70 to $261.72. At just around $277, the stereo is still too expensive.
At 1 PM, the stereo will be $235.55. Calculate the sales tax again:
6/100=x/235.55.
The sales tax on this one is only $14.33. Add this to $235.55. This gets you $249.88.
THEREFORE......
Calvin can afford the stereo at 1:00 PM. Henry's claim is not true, since the percentage of the stereo will change every time the price changes; just like 10% off of a $100 item is $90, 10% off of a $90 item is $81 and so on. The amount dropped isn't set.
Hope this helps!

Question 569103: why can't the size of the angle at the centre of a regular polygon be 25 degrees?
Answer by Alan3354(21555)   (Show Source):
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why can't the size of the angle at the centre of a regular polygon be 25 degrees?
------------
360/25 is not an integer.
A polygon can't have 14.4 sides.

Question 568483: If the measure of each interior angle of a regular polygon is five times the measure of each exterior angle, how many sides does the polygon have ?
Answer by stanbon(48516)   (Show Source):
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If the measure of each interior angle of a regular polygon is five times the measure of each exterior angle, how many sides does the polygon have ?
---
ext + int = 180 degrees
int = 5*ext
--
ext + 5ext = 180
est = 30 degrees
----
sum of the exterior angles is 360
# of exterior = 360/30 = 12
---
# of sides is 12
===================
Cheers,
Stan H.
=============

Question 568358:
A polygon has n sides.There of its exterior angles are 70 degree, 25 degree, 15 degree while the remaining (n-3) exterior angles are each equal to 50 degree.Find n.

affiliate network, pandora, limewire
Answer by stanbon(48516)   (Show Source):
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A polygon has n sides.There of its exterior angles are 70 degree, 25 degree, 15 degree while the remaining (n-3) exterior angles are each equal to 50 degree.Find n.
----
Sum of the exterior angles is always 360.
Equatiion:
(n-3)50+70+25+15 = 360
(n-3)50+110 = 360
(n-3)= 250/50 = 5
n = 8
=================
cheers,
Stan H.
=================

Question 567992: how do you use the distance formula for finding a polygon?
Answer by Alan3354(21555)   (Show Source):
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how do you use the distance formula for finding a polygon?
--------------
Where did you last see the polygon?

Question 567831: A regular polygon of 5 sides has vertex angles which measure how many degrees?
Answer by solver91311(12118)   (Show Source):
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A regular polygon of sides has interior angles that measure:

degrees

John

My calculator said it, I believe it, that settles it

Question 567634: A regular polygon has 33 sides. what is the size of each interior angle
Answer by Alan3354(21555)   (Show Source):
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A regular polygon has 33 sides. what is the size of each interior angle
----------
Each external angle = 360/33 degs
Int = 180 - external

Question 566920: how do i find the interior and exterior angles of a 900 sided regular polygon

Answer by Alan3354(21555)   (Show Source):
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how do i find the interior and exterior angles of a 900 sided regular polygon
-----------
The sum of exterior angles is 360 degs for all polygons.
360/900 = 0.4 degs
Interior angles = 180 - ext
= 179.6 degs each

Question 566763: I need to find the side length of a 6 sided polygon with an apothem of 14 in. so that I may find the area.
Please help me in simple language on HOW TO FIND A SIDE LENGTH to use in formula A=1/2aP.
Thank you so much!
Answer by scott8148(5879)   (Show Source):
You can put this solution on YOUR website!
a 6 sided polygon (hexagon) consists of 6 equilateral triangles joined at a common vertex (the center of the hexagon)

the side length you want is the side of an equilateral triangle that has an altitude of 14

the altitude of an equilateral triangle bisects the base and forms two congruent 30-60-90 right triangles

the ratio of the sides of a 30-60-90 triangle is ___ 1 : 2 : sqrt(3)

in this case, the ratio represents ___ (s / 2) : s : 14

so ___ 14 / [sqrt(3)] = s / 2

Question 566580: Please help me on this, i have a test on this next class and i have no idea what im supposed to do!
The ratio of the weight of an object on Mars to its weight on Earth is 9 to 25. If a person weighs 120 pounds on Earth, how much would the person weigh on Mars?
A flagpole casts a shadow of 8.5 meters long. If an algebra student 1.6 meters tall casts a shadow of 2.0 meters long at the same time and location, how tall is the flagpole in meters?
THANKS SO MUCH!!!! :DDDDDDDDDDDDDDDDDDDDDDDDDD
Answer by ankor@dixie-net.com(12684)   (Show Source):
You can put this solution on YOUR website!
The ratio of the weight of an object on Mars to its weight on Earth is 9 to 25.
If a person weighs 120 pounds on Earth, how much would the person weigh on Mars?
:
These are just ratio equations, quite easy.
let m = his weight on Mars
=
cross multiply
25m = 120 * 9
25m = 1080
m =
m = 43.2 lb on Mars
:
:
A flagpole casts a shadow of 8.5 meters long.
If an algebra student 1.6 meters tall casts a shadow of 2.0 meters long at the same time and location, how tall is the flagpole in meters?
:
Similar triangles, the corresponding sides have the same ratio
let f = height of the flag pole
=
Cross multiply
2f = 1.6 * 8.5
:
You should be able to finish this one, just like the 1st one

Question 566587: PLEASE HELP!!!!!!!! test next class on this!
A U.S nickel is composed of 3.9 grams of copper and only 1.2 grams of nickel. How many kg of copper must be combined with 4kg of nickel in the manufacture of a nickel coin?
In a town of 30,000 households, a survey was taken to estimate the number of households in which a certain TV program had been viewed. Of the 200 residences surveyed, the program had been seen in 64. Assuming that this was a representative sample, estimate the total number of households in the town in which the program was viewed.

THANKS SOOOOOOOOOOOOOOOOOOO MUCH! <3
Answer by bucky(2097)   (Show Source):
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These two problems can both be solved by using proportions. (A proportion is setting two fractions or ratios equal.)
.
Let's look at the first problem. We are given that a single nickel coin contains 3.9 grams of copper and 1.2 grams of nickel. So we can set up this ratio as a copper to nickel fraction, using the weight of copper (3.9 grams) as the numerator and the corresponding weight of nickel as the denominator. In other words we set up the fractional ratio:
.

.
Now we set this ratio equal to a second ratio. In this second ratio, we need to have the same units in the numerator as the first ratio. In the first ratio we chose to have the weight of copper in the numerator and the weight of nickel in the denominator. So our proportion will become:
.

.
We are told that the amount of nickel to be used is 4 kg. So we substitute 4 kg in the nickel denominator of the second ratio as follows:
.

.
Proportions can be solved by cross multiplying the numerator on one side by the denominator on the other side and setting the two products equal. In this problem we multiply the 3.9 numerator on the left side by the 4 denominator on the other side, and the resulting product of 3.9 times 4 is 15.6. Next we multiply the unknown number for copper (call it X) which is the numerator on the right side by the 1.2 denominator on the left side to get a product of 1.2X. Set the two products equal and you have:
.
15.6 = 1.2X
.
Solve for X by dividing both sides of this equation by 1.2. The result is:
.

.
Doing the division on the right side you get the answer:
.

.
And since we are relating kg to kg, the units on this answer is kg. So the answer is that X, the unknown amount of copper, must be 13 kg in order to mix with 4 kg of nickel to get the correct alloy for stamping out a bunch of nickels.
.
For your second problem you are told that in 200 residences, 64 had seen the show. Set up the proportion:
.

.
On the right side, the number of residences in the town is 30,000. Substitute this into numerator of the ratio on the right side to get the proportion:
.

.
(Note we substituted the X for the number of residences in the town that had seen the program.)
.
Cross multiply. First 200 times X = 200X. Then 30,000 times 64 = 1,920,000. Set the two products equal:
.

.
Divide both sides by 200 to solve for X and you have:
.

.
And doing the division on the right side results in:
.

.
So we can say that in the town of 30,000 residences the show was seen in 9,600 of them.
.
Hope this helps you to understand how you can work with proportions. Just make sure that the units of the two numerators are the same and the units of the two denominators are the same. If you do that, you don't have to worry about what should be on the top of the ratio and what is on the bottom. For example, in the first problem above we could have set up the proportion as:
.

.
to get:
.

.
and we would have gotten the same answer. (Note that the two cross products are still 1.2X and 15.6, the same as we got before.)
.
You can try it on the second problem also.
.

.

.
And you will still get the same answer of 9,600 residences in which the program was seen.
.
Good luck on your test. Study hard.
.

Question 566312: how do you find the degree meaure of an angle in a polygon
Answer by stanbon(48516)   (Show Source):
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insufficient information

Question 566197: How many sides does a polygon have with interior angles that equal 72?
Thanks
Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
How many sides does a polygon have with interior angles that equal 72?
Thanks
------------
3 sides --> 60 degs
4 sides --> 90 degs
---------
no such (regular) polygon

Question 566113: if you only had part of a shape and you wanted to find out how many sides the angle had in total.
how would you solve it???
Answer by Alan3354(21555)   (Show Source):
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if you only had part of a shape and you wanted to find out how many sides the angle had in total.
how would you solve it???
-------------
That's not clear.

Question 565636: The sum of the interior angle measures of a convex polygon is 1620 degrees How many sides does it have?
Answer by stanbon(48516)   (Show Source):
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The sum of the interior angle measures of a convex polygon is 1620 degrees How many sides does it have?
----------------------------
Sum = (n-2)180
1620 = (n-2)180
n-2 = 9
n = 11 sides
=================
Cheers,
Stan H.
===============

Question 565510: What is the sum of the measures of the interior angles of a regular polygon where a single exterior angle measures 72°?
Answer by ad_alta(170)   (Show Source):
You can put this solution on YOUR website!
The exterior angles sum to 360, so it must have 360/72=5 sides. The interior angles are therefore 108°.

Question 565511: A picture frame is shaped as a heptagon. The measure of one angle is 216°. The remaining interior angles are congruent. What is the measure of each remaining interior angle in the picture frame?
Answer by ad_alta(170)   (Show Source):
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The angles must sum to 900. Therefore 216+6x=900 for the angle 'x.' The angle must therefore be 114 degrees.

Question 565065: How Many Sides Are In The Polygon If The Measure Of The Interior Angle Is 156?
Found 2 solutions by kingme18, Alan3354:
Answer by kingme18(97)   (Show Source):
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Assuming that this is a regular polygon...
The easiest way to do this is to recall that the sum of the EXTERIOR angles is 360, and that an interior angle + its exterior angle = 180 (because they make a straight line). Thus, if the interior angles are each 156, the exterior angles are each 180-156=24. Now, if you take 360/24 (because each exterior angle is 24 and they need to add to 360), you get 15. Thus, there are 15 sides.

Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
How Many Sides Are In The Polygon If The Measure Of The Interior Angle Is 156?
===================
Ext angles = 180 - 156 = 24 degs
360/24 = 15 sides

Question 564996: If the interior angles of a polygon equals 1,440, how many sides does it have?
Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
If the interior angles of a polygon equals 1,440, how many sides does it have?
-------
1440/180 = 8
8 + 2 = 10 sides

Question 564681: how many regular polygons have an interior angle that measures between 100 and 149 degrees?
Found 2 solutions by richard1234, Alan3354:
Answer by richard1234(4789)   (Show Source):
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The sum of the degrees in an n-gon is 180(n-2), so for a regular polygon, the interior angle measure will be 180(n-2)/n. Therefore, we have

The "first" inequality yields .

The "second" inequality yields

Therefore, n is between 4.5 and 11.61; the only integer values of n that satisfy are 5, 6, ..., 11, or seven values.

Answer by Alan3354(21555)   (Show Source):
You can put this solution on YOUR website!
how many regular polygons have an interior angle that measures between 100 and 149 degrees?
----------
The exterior angles are between 31 and 80 degrees.
# of sides = 360/ext angle
360/32.7272 = 11 sides
360/36 = 10 sides
360/40 = 9 sides
360/45 = 8 sides
360/51.42 = 7 sides
360/60 = 6 sides
360/72 = 5 sides
-----------
7 polygons

Question 564508: The sum of the measures of the interior angles of a polygon Is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?
Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
The sum of the measures of the interior angles of a polygon Is five times the sum of the measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?
---
The sum of the exterior angles is ALWAYS 360 degrees.
--
So, sum of the interior angles is 5*360 = 1800 degrees.
----
Let n be the number of sides:
Equation:
(n-2)180 = 1800
n-2 = 10
n = 12 sides
====================
Cheers,
Stan H.
====================

Question 564495: how many sides does a 900 degrees polygon have

Answer by stanbon(48516)   (Show Source):
You can put this solution on YOUR website!
how many sides does a 900 degrees polygon have?
------
Let "n" be the number of sides:
Equation:
(n-2)180 = 900
---
n-2 = 5
---
n = 7
===========================
Cheers,
Stan H.
===============

Question 564088: Please help me solve this! i have a test on this next class and i dont know how to solve it! or polygons in general! Please help!
You are shown part of a convex n- gon. The pattern of congruent angles continues around the polygon.Use the Polygon Exterior Angles Theorem to find the value of n. Show all of your work and explain your process..
The picture i have no idea how to upload so i will describe it. It is an open, 7 sided shape that says that every other angle is equal to 125 degrees and the other angles that are not 125 degrees are 163 degrees.
I know its difficult without the diagram but please help me!!!!!! THANKYOU SOOOOOOOO MUCH!!!!!

Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
If the pattern continues, then the average measure of each interior angle should be (125+163)/2 = 144. Hence, for a polygon with n sides, we have

Solving for n, we obtain n = 10.

Question 564080: Please please por favor help me! Im in Honors Geometry and i have no idea how to solve any polygons and i have a test on this on Monday January 30 2012! please help! Thanks! :D
you've been asked to build a window frame for an octagonal window. To make the frame you'l cut identical trapezoid pieces. What are the measures of the angles of the trapezoids? Explain how you found these measures.
THANKS SOOO MUCH!!!! :D :D :D :D :D :D :D :D
Answer by richard1234(4789)   (Show Source):
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Most probably 135, 135, 45, 45, because you have isosceles trapezoids that make an octagon whose interior angles are 135. You'll have to draw it out to see.

Update: You can't cut an octagon in half to obtain two trapezoids. You might need three or four or more. To draw it, draw a regular octagon ABCDEFGH. The quadrilateral ABCH would be one of the trapezoids whose angles are 135, 135, 45, 45. These angles come from the fact that the measure of an interior angle of a regular octagon is 135.

Question 563955: In a quadrilateral ABCD,angle DAB=60 degrees and the other three angles are equal. The line CE is drawn parallel to BA to meet AD at E. calculate the angles ABC and ECD.
Answer by Edwin McCravy(6932)   (Show Source):
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The sum of the four internal angles of a quadrilateral is 360°. Since ∠A is 60°, that leaves 300° for the sum of angles ∠A, ∠BCD, and ∠D. Therefore they are 100° each since they are equal. ∠A and ∠CED are equal since they are corresponding angles when transversal AD cuts parallel lines AB and CE, and so ∠CED = 60°. The three interior angles of ᐃECD must have sum 180°, and since ∠CED = 60° and ∠D = 100°, they sum to 160°, leaving ∠ECD = 20° Edwin

Question 563889: Hello I am doing my homework and I need some help with this one question, What is the angle measure of a 20 sided polygon? Do you think you could help me? Thank You!
Answer by Alan3354(21555)   (Show Source):
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Hello I am doing my homework and I need some help with this one question, What is the angle measure of a 20 sided polygon?
--------------
The sum of exterior angles is 360 degs for all polygons.
360/20 = 18 degs each
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Each interior angle = 180 - Ext = 162 degs

Question 563479: find the measure of each angle of an equiangular nonagon
Answer by fcabanski(385)   (Show Source):
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A nonagon has nine sides.

The sum of the measures of the interior angles of a polygon is (n-2)*180 where n is the number of sides. In this case it's (9-2)*180 = 7*180 = 1260

This nonagon is equiangular, which means all the angles are equal. That means each angle measures total/#angles = 1260/9 = 140 degrees.

If you need help understanding math so you can solve these problems yourself, then one on one online tutoring is the answer ($30/hr). If you need faster solutions with guaranteed detailed answers, then go with personal problem solving ($3.50-$5.50 per problem). Contact me at fcabanski@hotmail.com

Question 563485: find the sum of the measures of the angles of a hexagon
Answer by fcabanski(385)   (Show Source):
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For any polygon (n-sided figure) the sum of the measures of the interior angles is (n-2)*180 where n is the number of sides.

A hexagon has 6 sides. n=6.
(6-2)*180 = 4*180 = 720 degrees.

If you need help understanding math so you can solve these problems yourself, then one on one online tutoring is the answer ($30/hr). If you need faster solutions with guaranteed detailed answers, then go with personal problem solving ($3.50-$5.50 per problem). Contact me at fcabanski@hotmail.com

Question 562746: What is the ratio of the measure of an interior angle to the measure of an exteror angle in a regular hexagon? A regular decagon? A regular n-gon?
I figured out that a hexagon is 3:2 and a decagon is 4:1 but I need help with the n-gon with n as any real positive number
Answer by scott8148(5879)   (Show Source):
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an exterior angle is ___ 360º / n

an interior angle is complementary to that ___ 180º - (360º / n)

[180º - (360º / n)] / (360º / n) ___ (n / 2) - 1

check your hexagon calculation...

Question 562780: If a/b = 5-x/x, then a+b/b = ?
Answer by issacodegard(60)   (Show Source):
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Hi,

This can be written,

Question 562621: For each polygon, how many diagonals can be drawn from one vertex? How many different diagonals can you draw from all the vertices of each polygon?
Quadrilateral-
Pentagon-
Hexagon-
Heptagon-
Octagon-
Nonagon-
Decagon-
N-gon-
Answer by solver91311(12118)   (Show Source):
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For any -gon, the number of diagonals that can be drawn from any one vertex is . The number of total diagonals is

John

My calculator said it, I believe it, that settles it

Question 560488: The measure of an exterior angle of a polygon is 20 degrees. Find the number of sides
Answer by solver91311(12118)   (Show Source):
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Not enough information. The total of the measures of the external angles of any polygon is 360 degrees, but without knowing that this is a regular polygon, just knowing that one of the exterior angles measures 20 degrees doesn't tell you anything about the measures of the rest of them. On the other hand if it is a regular polygon, then you know that all of the external angles are the same so you just divide 360 by 20.

John

My calculator said it, I believe it, that settles it

Question 560370: The sum of a regular polygon's angle measures is 1440 degrees.
What is the measure of one of the angles of the regular polygon?
Answer by Earlsdon(6098)   (Show Source):
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The sum (S) of the interior angles of a polygon of n sides is given by:
and S is given as 1440 so...
Divide both sides by 180.
Add 2 to both sides.
The regular polygon has 10 sides.
An interior angle (A) of a regular polygon of n sides is given by:
But and n = 10:

degrees.

Question 560250: is it possible to have a polygon whose sum of interior angle is
(1) 7 right angle
(2) 4500
Answer by Theo(2967)   (Show Source):
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the formula for the sum of the interior angles of a polygon is:
S = 180 * (n-2)
if n = 3 (triangle), then S = 180 * (3-2) = 180
if n = 4 (quadrilateral), then S = 180 * (4-2) = 360
from the formula for S, we can derive the formula for n as follows:
S = 180 * (n-2)
divide both sides of this equation by 180 to get:
S / 180 = n-2
add 2 to both sides of this equation to get:
n = (S/180) + 2
for the triangle, we get:
n = (180/180) + 2 which equals 1 + 2 which equals 3.
for the quadrilateral, we get:
n = (360/180) + 2 which equals 2 + 2 which equals 4.
if the sum of the interior angles is 4500, then the formula becoms:
n = (4500/180) + 2 which becomes:
n = 25 + 2 which becomes:
n = 27
i'm not sure what you mean by 7 right angle.
if you mean 7 * a right angle, then the sum would be 7 * 90 = 630 degrees.
the formula becomes:
n = (630/180) + 2 which becomes:
n = 3.5 + 2 which becomes:
n = 5.5
since n has to be an integer, the sum of angles equal to 630 degrees would not be possible.
if n is 5, the sum is 3 * 180 = 540 degrees.
if n is 6, the sum is 4 * 180 = 720 degrees.