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ACC. Geometry
Name
Proofs Unit Review
Per/Sec.
Date
1.
The ratio of the measures of two supplementary angles
is 45xx + 101 . Find the value of x.
2.
The measure of the complement of an angle is three times
the measure of the angle. What is the measure of the angle?
3.
Two angles that have degree measures that add to 90 are
called
angles.
4.
bisects ABC , m ABD = 2 x 15, and
Given BD
m CBD = x + 35, what is the measure of ABC ?
5.
The ratio of the measures of two complementary angles is
4 : 11. What are the measures of the two angles?
6.
The measure of the complement of an angle is one-sixth of
the measure of the supplement of the angle. What is the
measure of the angle?
7.
bisects ABC , m ABD = 2 x 10, and
Given BD
m CBD = x + 30, what is the value of x ?
8.
An angle is 73 smaller than its supplement. What are the
measures of the two angles?
9.
Find the value of x given:
m 1 = 6x 5
m 2 = 4x
m ABC = 120
is the angle bisector of TSV .
10. In the diagram, SU
m 1 = 4x 3 and m 2 = 2 x + 1. What is the value of x if
the measure of RSV is 96?
11. In the diagram, m 3 = 5 x + 50 and
the measure of 3?
m
WYZ = 8 x. What is
bisects MNO , m MNP = 7x 12, and m ONP = 4x + 5.
13. NP
What is the measure of MNO ?
12. Find the value of x given:
m 1 = 3x + y
m 2 = y + 90
1
= 2
is the angle bisector of RSU . If
14. In the diagram, ST
m RSV = 88 and m 1 = 25, what is the measure of 3?
Page 2
1 5. In the diagram, 3 and
bisects
straight line.
value of m 3?
YT
WYZ are a linear pair and form a
WYZ . If m 2 = 25, what is the
1 7. Which of the following could represent the sum of the
measures of two acute angles?
a) 1 74 b) 1 80 e) all of these values
c) 1 93 PT
MPQ
1 9. You are given that
bisects
= 2 k + 1 0 and m
= 6k
m
of k ?
MPT
TPQ
1 6. The measures of the complement of an angle and the
supplement of the angle are in the ratio 1 : 1 1 . What is the
measure of the angle?
1 8. The ratio of the measures of two supplementary angles is # .
What are the measures of the two angles?
d) 242 and that
2. What is the value
ST is the angle bisector of RSU .
20. In the diagram,
= 92 and
m
RSV
m
If
1 = 24, what is the measure of 3?
FHD
GHF
21 . The measures of the complement of an angle and the
supplement of the angle are in the ratio 1 : 1 6. What is the
measure of the angle?
22. In the diagram, m
= 1 0 x 7 and m
= 8 x + 9.
What is the degree measure of the smaller of the two angles?
23. The ratio of the measures of two complementary angles is
5 : 4. What are the measures of the two angles?
24. If the noncommon sides of two adjacent angles are opposite
rays, the angles form a( n)
.
Page 3
25. In the diagram,
m *:, ?
bisects *:, .
:+
If m
*:+ = 71 ,
what is
27. Find the value of x given:
m
28. The measure of the supplement of an angle is three times
the measure of the complement of the angle. What is the
measure of the angle?
m
m
1 = 9x
2 = 6x + 4
)*+ = 1 1 4
29. In the diagram,
the value of m
bisects /:- .
:.
/:- ?
26. One of two complementary angles is 25 larger than the
other. What is the measure of both angles?
If m
/:. = x,
what is
31 . The ratio of the measures of two supplementary angles is % .
What are the measures of the two angles?
:.
bisects
30. In the diagram, 58 54 , m
What is the measure of 2?
32. In the diagram,
is m /:. ?
856 = 54,
/:- .
If
and
m 457 = 56.
m /:- = 84,
what
Page 4
33. QZ is the angle bisector of $ PQR . Name two angles that
have equal measure.
34. Find the value of x given:
$1
m$ 1
= $2
= 2x + 2y
m$ 2 = 2 y + 50
35. Find the value of x given:
m$ 1 = x + 7
m$ 2 = 3 x 2
m$ 3 = 2 x 6
36. If two angles are complementary, then they are both
angles.
m$ PQR = 1 07
37. You are given that FH bisects $ EFG and that
m$ EFH = 2 x + 32 and m$ GFHX = 4x 1 0. What is the
measure of $ EFH ?
Determine whether each of the following statements is always, sometimes, or never true.
38. Two lines intersect to form adjacent angles.
39. An obtuse angle has a degree measure of 1 70.
40. The sum of the measures of two acute angles is greater than
the measure of one right angle.
41 . The two angles in a linear pair are adjacent to each other.
42. Two angles of a linear pair are both right angles.
43. Three angles whose degree measures sum to 1 80 are
supplementary angles.
44. Two vertical angles are supplementary.
45. A point in the exterior of one of two vertical angles is in the
interior of the other.
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