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Geometry - Verifying Angle Relationships
Congruent Supplements/Complements Theorems
Name________________________________
Date__________________Period__________
Complete each statement with always, sometimes, or never.
1. Two angles that are congruent are ______________ complementary to the same angle.
2. Two angles that are complementary to the same angle are ___________ congruent.
3. Two angles that are vertical are ______________ nonadjacent.
4. Two angles that are nonadjacent are _________________ vertical.
5. Two angles that are complementary ________________ form a right angle.
6. Two angles that form a right angle are _________________ complementary
7. Two angles that form a linear pair are ____________________ congruent.
8. Two angles that are supplementary are _____________ congruent.
9. Two angles that are supplementary are __________________ complementary.
10. Two right angles are _______________ supplementary.
11. Vertical angles are __________________ complementary.
12. Angles with a common side and a common vertex ______________ form a linear pair.
13. Find the measure of each numbered angle.
5 and A are complementary
6 and A are complementary
m5 = 2x + 2
m6 = x + 32
6
5
A
15. G and E are complementary. E and O are
also complementary. If mG = 5x – 1 and
mO = 3x + 23, find mE.
14. Find the measure of each numbered angle.
m7 = x + 20, m8 = x + 40, and m9 = x + 30
7
12
8 9
10
11
16. 7 and 8 are supplementary
8 and 9 are supplementary
m7 = 8x + 11 and m9 = 10x + 3. Find x and m9.
18. If 1 and 2 are complementary, 3 and 4 are
complementary, m2 = 4x + 3, and m3 = 5x – 7.
Find x and m3.
17. If ED bisects AEC , m2 = 18x + 9, and
m3 = 20x – 5, find the value of x and m2.
A
2
E3
1
4
D
F
B
A
1
Y
C
E
1
S
1
M
D
2
3
2
3
R
20. 1  3 , m2 = 2x + 5 and m4 = 4x – 11. Find x
and m3.
19. SC  SM and SO  SP . m1 = 4x + 2 and
m3 = 5x – 9. Find m1 and m2.
C
I
3
4
O
2
P
21. 6 and 7 are complementary. 7 and 8 are
complementary. If m6 = 2x – 4 and m8 =5x – 40,
find x, m6, and m7.
4
22. A and B are supplementary. C and D are
supplementary. If A  C and mB = -x + 60 and
mD = 5x, find x, mA, and mB.
23. BA  BC and CB  CD . If m2  m3, m1 = 7x – 30 and m4 = 3x + 6, find x, m1, and m3.
A
1
C
2
B
3
4
D