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Geometry
WS - Exploring Angles
Name___________________________
Date______________Period_________
adjacent angles
angle bisector
complementary angles
supplementary angles
vertical angles
Choose the word from the list above that is defined by each statement.
1. two angles whose measures have a sum of 180
2. two angles whose measures have a sum of 90
3. two angles whose sides are opposite rays
4. two angles that share a side but do not overlap
5. a ray that divides one angle into two angles with
the same measure
Use a word from the list above to complete each sentence.
6. If the measure of one angle in a pair of
measure of the other angle is 180 – n.
7.
never share a side.
8.
always share a side.
is n, the
9. Which of the following are a pair of vertical angles?
A. GBA and CBJ
C. ABM and MBC
B. GBA and GBM
D. ABJ and MBC
10. Which of the following are supplementary angles?
F. GBA and CBJ
H. ABM and MBC
G. GBA and GBM
J. ABM and MBC
Draw two angles that satisfy the following conditions.
11. The angles intersect in one
point
12. The angles intersect in four
points.
13. The angles intersect in a
segment.
OVER
Refer to the figure below for exercises 14-22.
14. Name two angles that have N as a vertex.
15. If MQ bisects PMN, name two congruent angles.
I

Q
P
16. Name a point on the interior of JMQ.
17. List all the angles that have O as the vertex.
J

O
M
K
18. List all the angles that have MN as a side.

N
R
L
19. If mPMO=55 and mOMN=65, what is the measure of PMN?
20. Is P a valid name for one of the angles? Explain.
21. Name a pair of angles that share exactly one point.
22. Is PN the same as NP ? Explain.
In the figure, BA and BC are opposite rays, and BE bisects ABD.
23. If mABE = 6x + 2 and mDBE = 8x – 14, find mABE.
E
24. Given that mABD = 2y and mDBC = 6y – 12, find mDBC.
D

A

B
25. Find mEBD if mABE = 12n -8 and mABD = 22n – 11.
26. If mABE = 9x – 1 and mDBC = 24x + 14, find mEBD.
27. Suppose mABE = 15y and mDBC = 45y – 30. Find the value of y.
28. If ABD is a right angle and mABE = 13x – 7, what is the value of x?

C
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