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Teacher: Mr. Joseph
Introduction to Angles
Name:__________________________
Period: ________ Date: ____________
Solve:
1)
2)
What does supplementary mean?
SILYM is a regular pentagon. What
is m SEI?
3)
C and G are congruent. m C =
30°. What is m G?
4)
A and W are complementary. m A
= 30°. What is m W?
5)
__
→
FY is bisected by LO.
6)
__
CT is bisected by AN.
If FL = x + 31 and LY = 5x + 19, what
is FY?
If CA = 5x + 2 and CT = 4x + 52, what
is AT?
Solve for x:
7)
(2x -3)°
(5x -8)°
8)
(12x -7)°
(2x + 3)°
9)
(13x -12)°
10)
(2x + 17)°
(5x + 16)°
(6x + 5)°
Solve:
11)
In JTQ, m Q = (-13x + 85)°, m T = 12)
(-2x + 60)°, and m J = (2x +
100)°. What is x?
13)
14)
m P = (x + 9)°, m N = (x + 15)°,
and m SIP = (-4x + 60)°. Solve for x.
m AWR = (x + 10)°, m PRW = (x +
9)°, and m PAW = (11x -107)°. Solve
for x.
15)
In NYW, m N = (-20x + 410)°, m
Y = (-18x + 324)°, and m W = (4x +
24)°. What is m N?
16)
m P = 71°, m N = 4°. Find m SIP.
m WFR = 113°, m PRF = 30°.
Find m RAW.
EasyWorksheet Step By Step Answers
User Name: J. Joseph
Form #46261171149
Practice Problems
1)
SILYM is a regular pentagon. What is m SEI?
All of the angles around the center (point E) are the same, and they sum to 360°, so
we take 360 and divide by 5 to get 72°
2) What does supplementary mean?
We use supplementary to mean that two angles sum to 180°
3) C and G are congruent. m C = 30°. What is m G?
Congruent means that the angles are the same.
So we get 30°
4) A and W are complementary. m A = 30°. What is m W?
Complementary means that the angles sum to 90°.
So we get 90 - 30 = 60°
5)
__
→
FY is bisected by LO.
If FL = x + 31 and LY = 5x + 19, what is FY?
Since FY is bisected, the picture actually looks like:
.
So LY = FL. And FY is twice that value.
So x + 31 = 5x + 19
-4x + 31 = 19
-4x = -12
x=3
But we need to make sure we answer the question! Plug back in x to get:
FY= 2(FL) = 2((3) + 31) = 68
6)
__
CT is bisected by AN.
If CA = 5x + 2 and CT = 4x + 52, what is AT?
Since CT is bisected, the picture actually looks like:
.
So AT = CA. And CT is twice that value.
So 2(5x + 2) = 4x + 52
10x + 4 = 4x + 52
6x + 4 = 52
6x = 48
x=8
But we need to make sure we answer the question! Plug back in x to get:
AT= CA = 5(8) + 2 = 42
7)
(2x -3)°
(5x -8)°
Since these are vertical angles, we set (2x -3)° equal to (5x -8)°:
(2x -3)° = (5x -8)°
Move all your terms so that your variable is on one side, and your constants are on the
other side of the equation:
2x + -5x = -8 + 3
Next combine your like terms to get: -3x = -5
Finally, divide both sides of the equation by -3:
So x = 5/3
8)
(12x -7)°
(2x + 3)°
Since these are vertical angles, we set (12x -7)° equal to (2x + 3)°:
(12x -7)° = (2x + 3)°
Move all your terms so that your variable is on one side, and your constants are on the
other side of the equation:
12x + -2x = 3 + 7
Next combine your like terms to get: 10x = 10
Finally, divide both sides of the equation by 10:
So x = 1
9)
(13x -12)°
(5x + 16)°
Since these create a linear pair, we know that (13x -12)° and (5x + 16)° are
supplementary:
(13x -12)° + (5x + 16)° = 180°
18x + 4 = 180
Move all your terms so that your variable is on one side, and your constants are on the
other side of the equation:
18x = 180 + -4
Next combine your like terms to get: 18x = 176
Finally, divide both sides of the equation by 18:
So x = 88/9
10)
(2x + 17)°
(6x + 5)°
Since these create a linear pair, we know that (2x + 17)° and (6x + 5)° are
supplementary:
(2x + 17)° + (6x + 5)° = 180°
8x + 22 = 180
Move all your terms so that your variable is on one side, and your constants are on the
other side of the equation:
8x = 180 + -22
Next combine your like terms to get: 8x = 158
Finally, divide both sides of the equation by 8:
So x = 79/4
11) In JTQ, m Q = (-13x + 85)°, m T = (-2x + 60)°, and m J = (2x +
100)°. What is x?
In a triangle, the angles sum to 180° so we set up the following equation:
180° = (-13x + 85)° + (-2x + 60)° + (2x + 100)°
180 = -13x + 85 + -2x + 60 + 2x + 100
180 = -13x + 245
-65 = -13x
5=x
So, x = 5
12) In NYW, m N = (-20x + 410)°, m Y = (-18x + 324)°, and m W = (4x +
24)°. What is m N?
In a triangle, the angles sum to 180° so we set up the following equation:
180° = (-20x + 410)° + (-18x + 324)° + (4x + 24)°
180 = -20x + 410 + -18x + 324 + 4x + 24
180 = -34x + 758
-578 = -34x
17 = x
So, x = 17
Filling this back in for N, we get 70°
13)
m AWR = (x + 10)°, m PRW = (x + 9)°, and m PAW = (11x -107)°. Solve for x.
In a triangle, the two opposite interior angles sum to the exterior angle. This means we
can set up an equation:
x + 10 + x + 9 = 11x -107
2x + 19 = 11x -107
Moving our constants to the right and any variables to the left, we get:
-9x = -126
So we end up with x = 14
14)
m P = (x + 9)°, m N = (x + 15)°, and m SIP = (-4x + 60)°. Solve for x.
In a triangle, the two opposite interior angles sum to the exterior angle. This means we
can set up an equation:
x + 9 + x + 15 = -4x + 60
2x + 24 = -4x + 60
Moving our constants to the right and any variables to the left, we get:
6x = 36
So we end up with x = 6
15)
m WFR = 113°, m PRF = 30°. Find m RAW.
Using the Triangle Sum Theorem, we get:
180° = m WFR + m PRF + m FAR.
180° = 113° + 30° + m FAR.
So m FAR = 37°.
RAW is a linear pair with FAR, so by the Linear Pair Postulate, these are
supplementary angles:
180° = m RAW + m FAR
180° = m RAW + 37°
So m RAW = 143°
16)
m P = 71°, m N = 4°. Find m SIP.
We can use the Triangle Sum Theorem to conclude:
m PIN = 180° - 71° - 4°
m PIN = 105°
But we are looking for m SIP!
We can use the fact that PIN and SIP are a linear pair, so they are supplementary.
m SIP = 180° - 105° = 75°
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