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Transcript
```Name
1-5
Class
Date
Practice
Form K
Exploring Angle Pairs
Use the diagram at the right. Is each statement true? Explain.
1
6
1. /5 and /4 are supplementary angles.
No; they are complementary.
5
2
4 3
2. /6 and /5 are adjacent angles.
Yes; they have a common side and vertex.
3. /1 and /2 are a linear pair.
Yes; they are adjacent angles whose noncommon sides are opposite rays.
Name an angle or angles in the diagram described by each
of the following.
4. a pair of vertical angles
lRPQ and lTPU
S
T
R
Q
40
U
P
5. supplementary to /RPS lSPU
To start, remember that supplementary angles are two angles whose measures
u
have a sum of 180 .
6. a pair of complementary angles lQPR and lRPS or lRPS and lUPT
To start, remember that complementary angles are two angles whose
u
measures have a sum of 90 .
7. adjacent to /TPU lSPT, lRPT, lQPU, lRPU, and lQPT
A
For Exercises 8–11, can you make each conclusion from the
information in the diagram? Explain.
8. /CEG > /FED
Yes; the arcs indicate they
are equal.
F
D
B
9. DE > EF
Yes; they are marked as O.
E
C
G
11. /ADB and /FDE are vertical angles.
no; not enough information
Yes; their sides are opposite rays.
Use the diagram at the right for Exercises 12 and 13.
12. Name two pairs of angles that form a linear pair.
Answers may vary. Sample: lNSO and lQSO; lNSP
and lQSP; lOSP and lRSP; lOSQ and lRSQ
13. Name two pairs of angles that are complementary.
lPSQ and lQSR, lPSQ and lNSO
P
Q
O
N
Prentice Hall Foundations Geometry • Teaching Resources
45
S
R
Name
Class
Date
Practice (continued)
1-5
Form K
Exploring Angle Pairs
)
14. Algebra In the diagram, XY bisects /WXZ.
Z
Y
a. Solve for x and find m/WXY. 5; 28
(5x 3)
W
b. Find m/YXZ. 28
(7x 7)
c. Find m/WXZ. 56
X
)
Algebra QR bisects lPQS. Solve for x and find mlPQS.
15. m/PQR 5 3x, m/RQS 5 4x 2 9 9; 54
16. m/PQS 5 4x 2 6, m/PQR 5 x 1 11 14; 50
17. m/PQR 5 5x 2 4, m/SQR 5 3x 1 10 7; 62
18. m/PQR 5 8x 1 1, m/SQR 5 6x 1 7 3; 50
Algebra Find the measure of each angle in the angle pair described.
19. The measure of one angle is 5 times the measure of its complement. 75 and 15
20. The measure of an angle is 30 less than twice its supplement. 70 and 110
21. Draw a Diagram Make a diagram that matches the
following description. Answers may vary. Sample:
3
2
•
•
/2 and /3 are a linear pair.
•
/2 and /4 are vertical angles.
•
/4 and /5 are complementary.
1
5
4
In the diagram at the right, mlHKI 5 48.
Find each of the following.
F
22. m/HKJ 90
23. m/IKJ 42
24. m/FKG 42
25. m/FKH 132
26. m/FKJ 138
27. m/GKI 138
K
J
48
I
Prentice Hall Foundations Geometry • Teaching Resources