Tutors Answer Your Questions about Polygons (FREE)
Question 994114: Number of sides of two polygons differ by 3. If their exterior angles differ by 20 then find the number of sides of each polygon
Answer by solver91311(20879) (Show Source):
Question 993325: Prove that the angles between adjacent diagonals at any vertex of an nsided regular polygon are equal and have the value 180/n.
Answer by ikleyn(988) (Show Source):
Question 992982: Each figure is a regular polygon. Expressions are given for two side lengths. Find the value of x.
a square: one side x2 + x and another side: x2 + 4
a hexagon: one side: x2 + 3x and another side x2 + x + 2
Answer by MathLover1(11324) (Show Source):
Question 992749: The ratio of the interior angle to the exterior angle of a regular polygon is 5:2. Find the number of the sides of the polygon
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! The ratio of the interior angle to the exterior angle of a regular polygon is 5:2. Find the number of the sides of the polygon
================
5x + 2x = 180
x = 180/7

Ext angles = 360/7
n = 360/(360/7) = 7 sides
Question 992503: ST is one side of the polygon and O is the center. What is the size of < SOT?
Answer by jim_thompson5910(33401) (Show Source):
Question 990236: Seven of the interior angles of a nonagon add up to 1020° and one of the remaining angles is twice the other. Find the size of each remaining angle
Answer by Theo(5548) (Show Source):
You can put this solution on YOUR website! one of the angles will be 80 degrees.
the other angle will be 160 degrees.
the sum of the angles of the nonagon will be equal to 1020 + 240 = 1260.
a nonagon has 9 sides.
the sum of the angles of the nonagon are equal to (92)*180 = 7 * 180 = 1260.
the sum of the angles of a nonagon is also equal to 9 * (180  360 / 9) which is equal to 9 * 140 which is equal to 1260.
both formulas lead to the same sum of angle of a nonagon (nine sided figure).
once you know that, it's a simple formula to derive the angles.
let one of the angle = x and the other angle = 2x.
their sum is 3x.
1020 + 3x = 1260
3x = 1260  1020
3x = 240
x = 80.
2x = 160.
Question 990044: the sum of the outer angles of a polygon is twice the sum of the inner angles?how many sides does it have?what if the sum of outer angles is half the sum of inner angles? and if the sums are equal?
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! the sum of the outer angles of a polygon is twice the sum of the inner angles?how many sides does it have?

The sum of the exterior angles is always 360 degs
> interior angles = 180 > a triangle.

what if the sum of outer angles is half the sum of inner angles?
Do the same way as above.

and if the sums are equal
See above.
Question 988767: find the perimeter of the regular polygon
given information:
one side is 5(x+2) and the other is 7x+4
Thanks
Found 2 solutions by MathTherapy, josgarithmetic: Answer by MathTherapy(4047) (Show Source):
You can put this solution on YOUR website!
find the perimeter of the regular polygon
given information:
one side is 5(x+2) and the other is 7x+4
Thanks
No polygon  regular or irregular  has 2 sides. Polygons start with 3.
Answer by josgarithmetic(13975) (Show Source):
Question 987678: Let x represent the side length of a square. Find a regular polygon with side length x whose perimeter is twice the perimeter of the square. Find a regular polygon with side length x whose perimeter is three times the length of the square.
I just can't figure out how to calculate that when I don't know what type of polygon and how many sides it has?? Thanks for any help
Found 2 solutions by macston, solver91311: Answer by macston(4006) (Show Source):
You can put this solution on YOUR website! x=length of side; n=number of sides
perimeter=(number of sides)(length of side)
Perimeter=nx
perimeter(square)=4x
Regular polygon with perimeter 2 times square:
perimeter=2 times perimeter of square=2(4x)=8x
Perimeter=nx
8x=nx
8=n Number of sides=8
ANSWER 1: The polygon is an octagon.
.
length of square=x
perimeter=3x
perimeter=nx
3x=nx
n=3 Number of sides=3
ANSWER 2: The polygon is a triangle.
Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
If the side lengths are the same, the only way for a polygon to have a perimeter twice as large as the square is for the polygon to have twice as many sides as the square. There are 4 sides on a square, so the polygon with twice the perimeter must have how many sides?
John
My calculator said it, I believe it, that settles it
Question 985738: if the exterior angle of a regular polygon is 55degrees what is the value of its interior angles
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! if the exterior angle of a regular polygon is 55degrees what is the value of its interior angles

1st, that's not possible.
Int = 180  Ext = 125

360/55 is not an integer > no such regular polygon is possible.
Question 985588: What is the angle of a 500 sided polygon
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! What is the angle of a 500 sided polygon

If it's a regular polygon, each exterior is 360/500 degs.
The interiors are 180  Ext.
Question 985335: Three of the exterior angles of an nsided polygon are 15, 25, 70, and the remaining exterior angles are 50 each. Find the value of n.
Answer by Edwin McCravy(13211) (Show Source):
Question 985194: One of the interior angles of the polygon with n sides is 124 degrees and the other (n1) interior angles are each equal to 142 degrees. Find the value of n.
Answer by srinivas.g(527) (Show Source):
You can put this solution on YOUR website! the sum of the interior angles of a polygon of n sides is 180(n  2).
124+(n1)*142= 180(n2)
124+142n142 =180n180*2
142n+124142 =180n360
142 n18=180n360
142n18+360 =180n
142 n+342=180n
342=180 n142 n
342=38 n
n=
9
Result : 9
Question 984961: 150n=180(n2)
Answer by ikleyn(988) (Show Source):
Question 984723: K=2
Dilation
Answer by Alan3354(47455) (Show Source):
Question 983785: find scale factor and the value of x,y,and z.quad Abcd congruent to quad EFgh
Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
Right, I'll just get out my crystal ball, tarot cards, and chicken bones so that I can peer into the mystic mists and discern the diagram you are working from. Please, when posting questions here, use your head for something besides a hat rack.
John
My calculator said it, I believe it, that settles it
Question 983593: The sum of the interior angle of a regular polygon is 16 rt angle s . determine the number of sides of the polygon
Answer by Boreal(1464) (Show Source):
Question 983226: In the figure above, OP Is a radius of the circle, PX is a tangent of the circle at point P, and the area of triangle OPX is 12. What is the area of the circle?
a. 16Pi
b. 12Pi
c. 18Pi
d. 24Pi
Link to image
http://152.46.13.240/MoodleContent/SATprep/Math%20Unit%207/Lesson%203%20Assignment/cb2.gif
Answer by ikleyn(988) (Show Source):
Question 983192: The difference between the exterior angles of two regular polygon having sides equal to n and n+1 is 12. Find the value of n
Answer by MathLover1(11324) (Show Source):
Question 982337: Interior angle of regular polygon is 3 times its exterior.
a)find the size of exterior angle
b)the sum of interior angles
c)what do we Call such polygon
Answer by solver91311(20879) (Show Source):
Question 982289: a student who was given a pentagon with four angle measures was asked to find the fifth angle the student said he would use [(n2)times 180]/n. will his method work?
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! That method might or might not work, depending on the pentagon. If not a regular pentagon, it can still be split into separate triangles.
Pick one vertex. Connect this with segments to the two nonadascent vertices. This will form THREE triangles.
180 degrees per triangle
3 triangles
The division by n WILL NOT WORK as a way to find the degrees per angle UNLESS this is a regular polygon. The above calculation is for 540 TOTAL degrees for the interior angles of the pentagon.
Question 982117: The two vertices that form the noncongruent side of an isosceles triangle are (5,3) and (2,3). What are the coordinates of the other vertex.
I am beyond lost. Thanks!
Found 3 solutions by Edwin McCravy, macston, josgarithmetic: Answer by Edwin McCravy(13211) (Show Source):
You can put this solution on YOUR website! The first tutor gave one possible solution, but there are infinitely many possible answers.
(1.5,5), (1.5,7), (1.5,0), (1.5,100), (1.5,100), etc.
the xcoordinate can only be 1.5, but the ycoordinate can be any number
except the two values that produce an equilateral triangle, since there are
no noncongruent sides to an equilateral triangle. Here are 4 solutions.
The last one is the one the first tutor gave.
Edwin
Answer by macston(4006) (Show Source):
You can put this solution on YOUR website! The other vertex that forms the triangle is on a line perpendicular to the segment at its midpoint.
.
Find the midpoint:
midpoint=((x1+x2)/2,((y1+y2)/2)
midpoint=((5+2)/2,(3+3)/2)
midpoint=((3/2),3)
.
Find the slope of the original segment:
m=slope
m=(y2y1)/x2x1
m=(33)/(2(5)=0/7=0
The line is horizontal.
.
The perpendicular line will be vertical, thus will have an undefined slope.
.
Equation for original line:
y=mx+b
y=3
.
The vertical line through the midpoint is x=(3/2)
Any point on the line x=(3/2) except ((3/2),3) can be connected to the given vertices to form an isosceles triangle.
Answer by josgarithmetic(13975) (Show Source):
You can put this solution on YOUR website! Look at the points on a cartesian coordinate system. They show the endpoints of the base of the isosceles triangle. The other vertex would be on the yaxis and would be the center of a circle. Notice that the given points form the segment of the triangle parallel to the xaxis. This makes identifying the point on the xaxis to be easy. Look for the midpoint of x coordinates of 5 and 2.
The vertex is ( 3/2, 0 ).
Question 980709: a polygon has n sides. Two of its exterior angles are 90 degrees and 60 degrees. The remaining Exterior angles are each 14 degrees. Calculate the value of n
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! a polygon has n sides. Two of its exterior angles are 90 degrees and 60 degrees. The remaining Exterior angles are each 14 degrees. Calculate the value of n

The sum of exterior angles = 360 degs
360  (90+60) = 210

210/14 = 15 angles
>n = 17 sides
Question 980595: Need to find the length of the long side of a pentagon which has three 132 degree angles and two 72 degree angles and the four given sides are all 65.08'
Answer by KMST(3791) (Show Source):
You can put this solution on YOUR website! .
On top of that pentagon, let me draw a few lines, and my favorite figures: right triangles.
.
The long (horizontal) side at the bottom of that pentagon, ,
is made of four segments:
, , , and ,
with and .
So .
From the right triangles on the left side, I get
(rounded) and (rounded).
Then,
Question 980527: The areas of two similar polygons are 147cm squared and 75 cm squared. What is the ratio of their perimeters?
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! The areas of two similar polygons are 147cm squared and 75 cm squared. What is the ratio of their perimeters?

A1:A2 = 147/75 = 49/25
P1:P2 = 7/5
Question 980345: A polygon has n sides
twp of the exterior angles are 41 each and five of the interior angles are 147 each
the remaining interior angles are 123.5 each.
Find the value of N
Answer by solver91311(20879) (Show Source):
Question 979974: A regular polygon first maps directly onto itself after rotating 10 degrees. How many sides does the polygon have?
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! A regular polygon first maps directly onto itself after rotating 10 degrees. How many sides does the polygon have?

360/10 = 36 sides
Question 979574: :whus7`h<
Answer by Alan3354(47455) (Show Source):
Question 979379: A hexagon has two sides each of length 3x inches. It has three sides each of length 2 inches. The sixth side has a length of 15 inches. If the perimeter of the hexagon is 135 inches, what is the value of x?
Answer by Edwin McCravy(13211) (Show Source):
You can put this solution on YOUR website! A hexagon has two sides each of length 3x inches.
1st side = 3x
2nd side = 3x
It has three sides each of length 2 inches.
3rd side = 2
4th side = 2
5th side = 2
The sixth side has a length of 15 inches.
6th side = 15
If the perimeter of the hexagon is 135 inches,
3x + 3x + 2 + 2 + 2 + 15 = 135
what is the value of x?
Solve the equation and that will be the value of x.
Edwin
Question 979314: The ratio of the interior angle to the exterior angle of a polygon is 5:2.how many sides has the polygon
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! The ratio of the interior angle to the exterior angle of a polygon is 5:2.how many sides has the polygon

5x + 2x = 180
x = 180/7

Ext angles = 2x = 360/7
# of sides = 360/Ext
# of sides = 7
Question 979233: The following polygons are given. All of the polygons are
regular polygons.
Polygon a. Convex 15gon
Polygon b. Convex 16gon
Polygon c. Convex 17gon
Polygon d. Convex 18gon
Polygon e. Convex 19gon
Polygon f. Convex 43gon
Polygon g. Convex 44gon
Polygon h. Convex 45gon
Polygon i. Convex 46gon
Polygon j. Convex 47gon
1. Which polygon(s) has (have) interior angles that are whole
numbers (a number that is not a fraction or a decimal)? Explain
why it is that way.
2. What happens to the value of the interior angles as the
number of sides of the polygon increases? Explain your answer.
3. What happens to the value of the exterior angles as the
number of sides of the polygon increases? Explain your answer.
4. Explain what happens to the total sum of interior angles
as the number of sides in the polygon changes?
5. Explain what happens to the total sum of exterior angles
as the number of sides in the polygon changes?
Found 2 solutions by solver91311, Edwin McCravy: Answer by solver91311(20879) (Show Source):
You can put this solution on YOUR website!
If is the number of sides and , then the measure of each interior angle is an integer.
As increases, the measure of the interior angles increases because gets closer to 180 as gets larger. A circle is the limiting shape as increases without bound so a circle is an infinitesided polygon with an infinite number of vertices with 180 degree interior angles. It was this idea that allowed Archimedes to approximate by sandwiching a circle between two 96sided polygons, one inscribed and the other circumscribed.
As increases, the measure of the exterior angles decreases because gets smaller as gets larger.
As increases, the total of the measures of the interior angles increases because gets larger as gets larger.
As increases, the total of the measures of the exterior angles remains constant because does not change as gets larger. Another way to put it is, no matter how many increasingly smaller turns you make, you still only go around one circle when you get back to where you started.
John
My calculator said it, I believe it, that settles it
Answer by Edwin McCravy(13211) (Show Source):
You can put this solution on YOUR website! The following polygons are given. All of the polygons are
regular polygons.
Polygon a. Convex 15gon
Polygon b. Convex 16gon
Polygon c. Convex 17gon
Polygon d. Convex 18gon
Polygon e. Convex 19gon
Polygon f. Convex 43gon
Polygon g. Convex 44gon
Polygon h. Convex 45gon
Polygon i. Convex 46gon
Polygon j. Convex 47gon
1. Which polygon(s) has (have) interior angles that are whole
numbers (a number that is not a fraction or a decimal)? Explain
why it is that way.
The sum of the interior angles of a polygon of nsides is
Since the polygons are regular, all the interior angles are the same,
so each one is that expression divided by n
That must be equal to a whole number, say, W. Since n does not divide
evenly into n2, it must divide evenly into 180°. So we go through
the list to see which numbers divide evenly into 180°:
Polygon a. Convex 15gon, yes, since 15 divides evenly into 180°.
Polygon b. Convex 16gon, no
Polygon c. Convex 17gon, no
Polygon d. Convex 18gon, yes, since 18 divides evenly into 180°.
Polygon e. Convex 19gon, no
Polygon f. Convex 43gon, no
Polygon g. Convex 44gon, no
Polygon h. Convex 45gon, yes, since 45 divides evenly into 180°.
Polygon i. Convex 46gon, no
Polygon j. Convex 47gon, no
2. What happens to the value of the interior angles as the
number of sides of the polygon increases? Explain your answer.
So the value of the interior angles approaches 180° as the number
of sides of the polygon increases.
3. What happens to the value of the exterior angles as the
number of sides of the polygon increases? Explain your answer.
The sum of the exterior angles of any polygon is 360°. So
each one of a regular polygon is
So the value of the exterior angles approaches 0° as the number
of sides of the polygon increases.
4. Explain what happens to the total sum of interior angles
as the number of sides in the polygon changes?
5. Explain what happens to the total sum of exterior angles
as the number of sides in the polygon changes?
Edwin
Question 978878: each of the 5 angles is equal to 172 degree and the other angle is 160 each the number of sides of the polygon is
Answer by Alan3354(47455) (Show Source):
You can put this solution on YOUR website! each of the 5 angles is equal to 172 degree and the other angle is 160 each the number of sides of the polygon is

5*172 = 860 degs
860 + (n5)*160 = (n2)*180
860 + 160n  800 = 180n  360
420 = 20n
n = 21 sides

5*172 + 16*160 = 3420
180*(21  2) = 3420
Question 978897: please help me to solve this question :
can 35 degree be the exterior angle of a regular polygon
Answer by jim_thompson5910(33401) (Show Source):
You can put this solution on YOUR website! n = 360/E
n = 360/35
n = 10.2857142857142
The result 10.2857142857142 is NOT a whole number. We cannot have a fractional number of sides.
So a 35 degree exterior angle is NOT possible for a regular polygon.
Question 978793: A regular polygon first maps directly onto itself after rotating 20 degrees. How many sides does the polygon have?
Answer by Fombitz(25151) (Show Source):
Question 978550: If a regular polygon has an angle of rotational symmetry that is 40° how many sides does the polygon have
Answer by josgarithmetic(13975) (Show Source):
Question 977524: The sum of the measures of the angles of any quadrilateral is 360°. The measures of ∠A and ∠B are the same. The measure of ∠C is 17° greater than the measure of ∠A, and the measure of ∠D is 37° less than ∠B. Find the measure of ∠A, ∠B, ∠C, and ∠D.
Found 2 solutions by solver91311, josgarithmetic: Answer by solver91311(20879) (Show Source): Answer by josgarithmetic(13975) (Show Source):
Question 976917: If the length of side a is 6 centimeters, the length of side b is 4 centimeters, and the length of side c is 7 centimeters, what is the measure of ∠B? Round your answer to two decimal places.
Answer by Cromlix(3061) (Show Source):
You can put this solution on YOUR website! This a triangle I take it.
Side a = 6cm
Side b = 4cm
Side c = 7cm
Find angle B
Using Cosine Rule
Cos B = (a^2 + c^2  b^2)/ 2ac
Cos B = (6^2 + 7^2  4^2)/ 2 x 6 x 7
Cos B = (36 + 49  16)/ 84
Cos B = 69/84
Cos B = 0.8214
Angle B = 34.77 degrees (2 decimal places)
Hope this helps :).
Question 976667: The interior angle of a regular polygon is thrice the exterior angle .how many sides has the polygon
Answer by htmentor(912) (Show Source):
You can put this solution on YOUR website! The sum of the interior and exterior angles must be 180 deg.
Let x = the measure of the exterior angle
Then x + 3x = 180 > 4x = 180 > x = 45
The exterior angles of a regular polygon add up to 360, which means each exterior angle is 360/n [n=number of sides]
So we have 360/n = 45 > n = 360/45 = 8
So the polygon is an octagon (8 sides)
Question 976283: Here is my question:
A rhombus ABCD has a perimeter of 32cm and a diagonal AC of length 8cm. What is the exact length of diagonal BD?
Thank you very much! :)
Answer by dkppathak(298) (Show Source):
You can put this solution on YOUR website! A rhombus ABCD has a perimeter of 32cm and a diagonal AC of length 8cm. What is the exact length of diagonal BD?
perimeter of rhombus =32 let side of rhombus is a than perimeter will be 4a
4a=32
a=8
diagonal of rhombus bisect each other at 90 degree let other diagonal 2x
1/2 of given diagonal will be =1/2 of 8= 4 cm and 1/2 of other diagonal will be x
using Pythagoras theorem
8^2= X^2+4^2
6416=x^2
48=x^2
X=sqrt of 48= 4 sqrt3
length of other diagonal will be 2x= 8sqrt3

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