1. Angle Relationships in Circles
12-5
Angle Relationships in Circles
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
Holt Geometry

2. 1. Identify each line or segment that intersects F.
Warm Up
1. Identify each line or segment that intersects F.
Find each measure.
2. mNMP
3. mNLP
chords: AE, CD
secant: AE
tangent: AB
110°
55°

3. Objectives
Find the measures of angles formed by lines that intersect circles.
Use angle measures to solve problems.

5. Example 1
Find each measure.
mEFH
= 65°

6. Example 1
Find each measure.

7. Example 2
Find each measure.
mSTU
= 83

8. Example 2
Find each measure.

10. Example 3
Find each measure.
mAEB
= 126

11. Example 4
Find each angle measure.
mABD

12. Example 5
Find each angle measure.
mRNM
mRNM = 180° – MNQ
mRNM = 180° – 158° = 22°

14. Example 6
Find the value of x.
= 40
= 63

15. Example 7
Find the value of x.
50° = 83° – x
x = 33°

16. Example 8
Two of the six muscles that control eye movement are attached to the eyeball and intersect behind the eye. If mAEB = 225, what is mACB?

18. Substitute 180 – 113 for mXVY and 68 for mWZ
Example 9 V U
Find
Step 1 Find
If a tangent and a secant intersect on a  at the pt. of tangency, then the measure of the  formed is half the measure of its intercepted arc.
Substitute 180 – 113 for mXVY and 68 for mWZ
Multiply both sides by 2.
Subtract 68 from both sides.

19. Substitute the given values.
Example 5 Continued V U
Step 2 Find
Thm
Substitute the given values.
Multiply both sides by 2.
Add 66 to both sides.

20. Example 10
Find mLP
Step 1 Find
Step 2 Find