LESSON

Date

Class

Practice A

11-5 Angle Relationships in Circles

In Exercises 1–3, match the letter of the drawing to the formula for finding the measure of the angle. 1 B A. 1. m ABC __ (mAC mDE ) 2

2. m ABC

1 __ (mAC 2

m DE )

C

B.

3. m ABC

1 __ mAB 2

A

C.

Find each measure. 4. m FGH 5. m IJ 6.

45° 150°

7.

m QPR

55°

m YUV

116°

8. Some cities in Europe are thousands of years old. Often the small center of the old city is surrounded by a newer “ring road” that allows traffic to bypass the old streets. The figure shows a circular ring road and two roads that provide access to the old city. Find m CBD. Find the value of x. 9.

82°

40

10.

67

Complete Exercises 11–13 in order to find m ECF.

_

11. Find m DHG. (Hint: DF is a straight segment.) 12. Find mEF. 13. Find m ECF.

96° 134° 38°

Holt Geometry

Copyright © by Holt, Rinehart and Winston. All rights reserved.

35

Name

LESSON

Date

Class

Practice B

11-5 Angle Relationships in Circles

Find each measure. 1. m ABE mBC

64° 96°

2.

m LKI mIJ

119° 42°

3.

m RPS

130°

4.

94° 68°

m YUX

99°

Find the value of x. 5.

° 116°

64

6.

173°

° 79°

47

7.

8

8.

113° 23° °

45

9. The figure shows a spinning wheel. The large wheel is turned by hand or with a foot trundle. A belt attaches to a small bobbin that turns very quickly. The bobbin twists raw materials into thread, twine, or yarn. Each pair of spokes intercepts a 30° arc. Find the value of x.

°

60

Find each measure. 10.

56° 39°

11.

30° 81°

70°

75°

m DEI mEF

66.5° 115°

36

m WVR mTUW

84° 192°

Holt Geometry

Copyright © by Holt, Rinehart and Winston. All rights reserved.

Name

Date

Class

Name

Date

Class

Practice A LESSON 11-5 Angle Relationships in Circles

In Exercises 1–3, match the letter of the drawing to the formula for finding the measure of the angle. � 1 � B A. 1. m�ABC � __ (mAC � mDE ) � 2 � �

Practice B LESSON 11-5 Angle Relationships in Circles

Find each measure. 1.

� �

����

�

���

�

m�ABE � mBC �

�

64° 96°

2.

�

���� ���

m�LKI �

�

� � �

mIJ �

�

119° 42°

���

�

�

� 1 � 2. m�ABC � __ (mAC � m DE ) 2

C

A

B.

� �

� � �

�

� �

3.

�

���

� �

m�RPS �

130°

4.

�

68°

� � �

94°

m�YUX �

99°

�

1 � 3. m�ABC � __ mAB 2

C.

� �

����

�

�

Find the value of x. 5.

�°

116°

Find each measure.

4. m�FGH � 5. m�IJ �

�

�

45° 150°

� �

��� ���

�

64

6.

173°

�°

79°

47

�

�

6.

�

���

� �

���

7.

���

� � � �

����

� �

�

7.

8

���

8.

113° 23°

45

�°

m�QPR �

55°

m�YUV �

�

116°

����

8. Some cities in Europe are thousands of years old. Often the small center of the old city is surrounded by a newer “ring road” that allows traffic to bypass the old streets. The figure shows a circular ring road and two roads that provide access to the old city. Find m�CBD.

� � �

���

��

����

��������

�

82°

9. The figure shows a spinning wheel. The large wheel is turned by hand or with a foot trundle. A belt attaches to a small bobbin that turns very quickly. The bobbin twists raw materials into thread, twine, or yarn. Each pair of spokes intercepts a 30° arc. Find the value of x.

�°