Practice with Angles in Circles
- Tangent/Chord and Intersecting Chords
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Solve the following problems dealing with angles in circles.

(Do not assume diagrams are drawn to scale.)

1.

Given tangent , find x.

Choose:

30
60
120
240




 

2.

Given tangent , find x.

Choose:

25
50
100
260



 

3.

Given tangent , find x.
Hint:  Find y first.

Choose:

72
108
144
216

 

 

4.

Given tangent , find x.
Hint:  Find y first. 

Choose:

30
60
150
300

 

 

5.

Given two intersecting chords, find x.   

Choose:

20
40
60
80

 

 

6.

Given diameter and chord, find x.   

Choose:

30
50
100
110

 

 

7.

Given diameter perpendicular to a chord, find x.     

Choose:

30
60
90
120

 

 

8.

Given diameter perpendicular to a chord, find y.     

Choose:

30
60
90
180

 

 

9.

The segment through point A is tangent to the circle at A.

Find x.     

Choose:

54
72
108
144

 

 

10.

Two chords intersect within a circle to form an angle whose measure is 53°.  If the intercepted arcs are represented by
 3x + 3 and 10x - 14, find the measure of larger of these two arcs.

Choose:

9
13
30
76

 

 

11.

A small round plate falls off of the china closet and breaks.  The diagram below shows one of the broken pieces.  is tangent to at B and degrees.  What is the measure in degrees of the arc , the outside edge of the broken piece?

Choose:

45
60
90
180