Triangle and Holt Geometry Copyright
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.
�°
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