Questions on Geometry: Angles, complementary, supplementary angles answered by real tutors!

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All are right angles except the three angles 
inside the triangle in the upper part of the "A":



Edwin

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let angles be a and b
:
a+b=180...eq 1
a=b+12....eq 2
:
take a's value from eq 2 and plug it into eq 1
:
b+12+b=180
:
2b=168
:
degrees
:
degrees

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Isosceles triangles have two equal sides and one side that is not equal.
Side LM = side LN.
3x - 2x = 2x + 1
3x - 2x = 2 + 1
x = 3

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In an equilateral triangle, all sides are equal,
x+5=3x-9=2x-2
Take x+5=3x-9 and solve for x
14=2x
Solve for x
x=7
Take 3x-9=2x-2 and solve for x
x=7
So x=7
I hope that this helps.

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I think what you need help with is actually the definition of supplemental angles. Two angles are supplements of each other if their sum is 180 degrees.

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Please tell the actual problem so that I may help you.

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Remember the conversion:


Then, 125deg,20min,30sec --------->working problem


Get LCD for those with fractions to add:

Reduce fraction by dividing both num. & den. by 60:

125 & 20.5/60 degrees ------> ANSWER, OR
Why the fraction part is doubled?
It doesn't matter -- doubled, tripled,quadrupled, or even times 10. Just remember whatever you do on the numerator, also do it on the denominator so the process is not change. Let' see:
, doubled
, tripled
, times 10
The ANSWER NEVER changed.
thank you,
Jojo

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it is called a hexagon

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Let x be the measure of AOX. Then COX is also x. Since AOB is 90, then BOC = 90 - 2x. Since COD is also 90, then BOD = 90 - (90 - 2x) = 2x. Finally, BOY is half that, or x. Therefore, since AOX and BOY are both x, then AOX = BOY. which was what we wanted

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In isosceles triangle CDE, angle C is thirty-nine degrees more than angle D. angle C is one of the congruent angles. What is the measure of each angle in triangle CDE?
-------------------
Let the vertex angle be "x" degrees.
Each base angle is "x+39" degrees.
-----------
EQUATION:
x + 2(x+39) = 180
3x + 78 = 180
3x = 102
x = 34 degrees (vertex angle measure)
x+39 = 73 (each base angle meansure)
===============================
Cheers,
Stan H.

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This is how I was taught:
3x + 15 | 4x + 12
Set the equation to 0.
3x + 15 = 0 | 4x + 12 = 0
-15 -15 | -12 -12
Subtract by 15. | Subtract by 12
3x = -15 | 4x = -12
/3 /3 | /4 /4
Divide by 3 | Divide by 4
x=-5 | x=-3
I could be wrong, but I'm pretty sure it's right.

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Can you post the problem you are talking about?
Cheers,
Stan H.

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One of two supplementary angles is 8 more than the other. Find the measure of the larger angle.
==========================================================
Since the angles are supplementary, then they add up to 180.
Let x = smaller angle
Let x + 8 = larger angle
We now have this:
x + x + 8 = 180
2x + 8 = 180
2x = 180 - 8
2x = 172
x = 172/2
x = 86
The larger angle is x + 8 and I just x to be 86.
So, the larger angle is 86 + 8 = 94

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You cannot have a 180 degree angle in a triangle.
The sum of the angles is always 180 but no one
angle can be 180.
Cheers,
Stan H.

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You are given 4 sides on the rectangle. Three on the triangle.
The perimeter of a polygon is the sum of its sides.
=
=
You are told the two polygons have the same perimeter. So
collect like terms


So the rectangle is 4 x 5
and the triangle is equilateral (all 3 sides are a length of 6.
Each has a perimeter of 18

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The area of a triangle is given by
If you know the triangle is a right triangle, then you can just use the two 'shorter' sides. Let the shortest side be b and the middle length side be h.
You are given that the sides are in ratio x:4x-1:4x+4
So the longest side is 4x+4
That makes the short side, b = X = 3
The middle length side, h = 4x-1 = 12-1 = 11


square units (whatever units x is in (the problem doesn't say

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two angles of a triangle are 30 degrees and 50 degrees, what is the measure of the third angle?
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3rd angle = 180-(30+50) = 180 - 80 = 100 degrees
===================
Cheers,
Stan H.

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supplementary angles =180
complementary angles =90
:
128+s=180--->degrees
:
:
:
15+c=90----->degrees

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What is the angle between the hour and the minute hands if the time is 8:20?
----------------
Draw the picture. There are 12 segments around the clock. Each segment
has 360/12 = 30 degrees.
If you assume the hour hand stays on 8 even when it is 8:20
the angle is 4*30 degrees = 120 degrees.
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If you assume the hour hand moves (1/3) of the segment as the minute hand
moves to 20 after the hour, the angle is 120+(1/3)30 = 130 degrees.
------------------
Cheers,
Stan H.

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What is the angle between the hour and the minute hands if the time is 8:20?
-------------------------
The minute hand is 1/3 of a revolution from straight up, or 120º
The hour hand makes one rev in 12 hours, so it have rotated 360º*((8 1/3)/12) degrees.
360º*((8 1/3)/12) = 30*(8 1/3) = 250º
250 - 120 = 130º

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only if its a square. All other diamond shapes will be paralleograms where consecutive angles will be supplementary(equal 180 degrees)

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You have the right idea!
With two intersecting lines as you describe with the top and bottom angles, which are called "vertical angles", equal to 102 degrees. The other two angle are 180 - 102 = 78 degrees each. These two angles (102 degrees and 78 degrees) are called "supplementary angles" and two supplementary angles add up to 180 degrees.

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angle 1 and 2 are complementary. If angle 1 was eight degrees less and angle 2 was fifty-seven degrees more, then they would be of equal measure. What are the measures of the two angles?
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Let angle 1 be "x"; then angle 2 is "90-x"
EQUATION:
x-8 = 90-x + 57
2x = 155
x = 72.5 degrees
90-x = 17.5 degrees
===============
Cheers,
Stan H.

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we have to be able to see other info to be able to tell what you are referring to....supplementary angles add up to 180 degrees. hope that info helps

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x=larger angle
1/3x+7=smaller angle
x+1/3x+7=143
Subtract 7 from both sides

x+x1/3=136
1+1/3=4/3
4/3x=136

multiply each side by 3/4

x=(136)(3/4)
x=102
Let's doublecheck our answer
smaller angle is (1/3)(102)+7=41

102+41=143

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how do I graph these two equations on a rectangular coordinate system
2x = y - (6x8)
2x = y - 48
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That's one equation. It's a linear equation, so its graph will be a straight line.
To graph it, find any 2 points.
Set x = 0 and find y. Then set y=0 and find x.
@x=0, y = 48
@y=0, x = -24
Plot the 2 points, (0,48) and (-24,0) and draw a straight line thru them. Or find any other points and do it.

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remember the hexagon is composed of 4 triangles so sum of the interior angles are 180(4)=720 since there are 6 angles divide 720/6=120 degrees for each interior angle of a REGULAR hexagon

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find the measure of one interior angle of a regular hexagon?
----------------------------
The sum of the 6 EXTERIOR angles = 360
Each exterior angle = 360/6 = 60 degrees
----------
Each interior angle is the supplement of a 60 degree exterior angle.
Therefore, each interior angle = 180-60 = 120 degrees
======================
Cheers,
Stan H.

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the 3 angles must equal 180
:
B+118+54=180
:
degrees

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i)find the value of x. x degrees, 80 degrees and 30 degrees
-------------------------
That makes no sense at all. x could be 1 degree, or 5,555 degrees.

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I imagine we are talking about a triangle. Based on that assumption
:
the 3 angles must equal 180 degrees
:
x+55+50=180...solve for x
:
degrees

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what is one of the complementary angles is three more than two that twice the other? find the measure of each?
.
If two angles are complementary, the sum of the two angles equal 90 degrees.
.
Let x = one angle
then
2x+3 = other angle
.
x + 2x+3 = 90
3x+3 = 90
3x = 87
x = 29 degrees (one angle)
.
Other angle:
2x+3 = 2(29)+3 = 58+3 = 61 degrees

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If 9x* and (5x+62)* are the measures of complementary angles, what is the measure of each angle?
---------------
9x + 5x+62 = 90
14x = 28
x = 2
---------
1st angle: 9x = 18
2nd angle: 5x+62 = 10+62 = 72
===============================
Cheers,
Stan H.

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If the non-base angle of an isosceles triangle has a measure of 70*, what is the measure of each base angle?
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The sum of the three angles is 180.
The base angles are equal.
70 + 2x = 180
2x = 110
x = 55 degrees (each base angle is 55 Degrees
======================
Cheers,
Stan H.

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Let the angle = A.
Its supplement is (180-A) and its complement is (90-A).
From the problem description you can write"
(180-A) = 6(90-A)+5 Simplify and solve for A
180-A = 540-6A+5
180-A = 545-6A Add 6A to both sides.
180+5A = 545 Subtract 180 from both sides.
5A = 365 Divide both sides by 5.
A = 73 degrees.

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According to my TI-30XIIS calculator:
sin(-11π/12)=-0.050240715 ans.

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Note: 660 degrees is a coterminal angle to -60 degrees





So

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Use Fundamental Identities and or the Complementary Angle Therom to find the exact value of the expression. If tan^2 Θ=9, find the exact value of sec^2 Θ.
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sec^2 = tan^2 + 1 (Is that a fundamental identity?) If not, use:
sin^2 + cos^2 = 1 and divide thru by cos^2.
--------------
sec^2 = 10

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It's impossible to draw your diagram here but let's see if I can explain it.
Imagine you're in the cockpit of the plane. It is flying at a height of 1240m. Looking down, at a distance, he sees the aircraft carrier (at an angle of 48 deg 22 min).
.
This basically forms a "right triangle" and we're looking for the hypotenuse.
.
Converting 48 deg and 22 min to a decimal:
48 + 22/60 = 48.3667
.
Applying trigonometry:
sin = opposite/hypothenuse
.
Let x = distance to carrier
.
sin(48.3667) = 1240/x
xsin(48.3667) = 1240
x = 1240/sin(48.3667)
x = 1240/0.7474
x = 1659.059 meters

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The complement of an angle and the angle add together to get 90 degrees.
If the angle is represented by x then the complement will be x - 10 because the complement is 10 degrees less than x.
The two angles add to make 90 degrees so



so x = 50 degrees
The complement will be 10 degrees less which is 40 degrees.

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if angle 1 equals 62 and angle 1 and angle 2 form a linear pair, find angle 2
.
If two angles form a "linear pair", it means the sum of the two angles equals 180 degrees (forming a straight line).
.
Let x = measure of angle 2
then
62 + x = 180
x = 180-62
x = 118 degrees (measure of angle 2)

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Do you have a protractor?
If not, get one at the local 99 cent store.
Measure 75 degrees using the protractor and you're done.
Keep in mind that 75 degrees is found in quadrant 1 and measures 15 degrees less than 90 degrees.

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Let the angle whose supplement you are trying to find = A
The supplement of angle A is (180-A) and 58 degrees more than that is:
(180-A)+58.
Now you have enough to write an equation that will let you find the angle A.
A = (180-A)+58 Simplify this to:
A = 180+58-A Add A to both sides.
2A = 238 Divide both sides by 2.
A = 119 degrees. But you are asked to find the supplement of A.
180-A = 180-119 = 61 degrees.
Check:
A = (180-A)+58 Substitute A = 119.
119 = (180-119)+58
119 = 61+58
119 = 119 It checks!

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2 angles make up a supplementary angles. Lets call them A and B,and the total of A and B has to total 180 degrees(definition of supplementary angles).
so A+B=180
we also know that one angle(makes no difference which one in this case) is 58 degrees more than the other so
A=B+58 substitute this A value back into the 1st equation
(B+58)+B=180
2B=180-58
2B=122

A=61+58=

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A Platonic solid is a solid all of whose face are regular and congruent polygons.
There are five of these:
A Tetrahedron. Four faces, each an equilateral triangle.
A Hexahedron (Cube). Six faces, each a square.
An Octahedron. Eight faces, each an equilateral triangle.
A Dodecahedron. Twelve faces, each a regular pentagon.
An Icosahedron. Twenty faces, each an equilateral triangle.