1. Apply Other Angle Relationships in Circles
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
Solve for x.
1. 2x =
ANSWER 58
2. x = ( 360 – 120) = 0
1 2
ANSWER
120
– x = ((2x + 4) + 28)
1 2
ANSWER 82

3. Warm-Up
4. One-half of the measure of an angle plus the angle’s supplement is equal to the measure of the angle. Find the measure of the angle.
ANSWER
120

4. Example 1
Line m is tangent to the circle. Find the measure of the red angle or arc.
SOLUTION = 12
(130o) a.
m 1
= 65o b.
m KJL = 2
(125o)
= 250o

5. Guided Practice
Find the indicated measure.
1. m1
105°
ANSWER

6. Guided Practice
Find the indicated measure.
2. mRST
196°
ANSWER

7. Guided Practice
Find the indicated measure.
3. mXY
160°
ANSWER

8. The chords JL and KM intersect inside the circle.
Example 2
Find the value of x.
SOLUTION
The chords JL and KM intersect inside the circle. x° = 12
(mJM + mLK)
Use Theorem x° = 12
(130° + 156°)
Substitute. x
= 143
Simplify.

9. The tangent CD and the secant CB intersect outside the circle.
Example 3
Find the value of x.
SOLUTION
The tangent CD and the secant CB intersect outside the circle.
m BCD
(mAD – mBD) = 12
Use Theorem = 12
(178° – 76°) x°
Substitute.
= 51 x
Simplify.

10. Example 4
The Northern Lights are bright flashes of colored light between 50 and 200 miles above Earth. Suppose a flash occurs 150 miles above Earth. What is the measure of arc BD, the portion of Earth from which the flash is visible? (Earth’s radius is approximately 4000 miles.)
SCIENCE

11. Because CB and CD are tangents, CB AB and CD AD
Example 4
SOLUTION
Because CB and CD are tangents,
CB AB and CD AD
Also, BC DC and CA CA . So, ABC ADC by the Hypotenuse-Leg Congruence Theorem, and
BCA DCA.Solve right CBA to find that m BCA
74.5°. = 12
m BCD
(mDEB – mBD)
Use Theorem
149° 12
[(360° – x°) –x°]
Substitute. x 31
Solve for x.
The measure of the arc from which the flash is visible is about 31°.

12. Guided Practice
Find the value of the variable. 4.
y = 61
ANSWER

13. Guided Practice
Find the value of the variable. 5.
a = 104
ANSWER

14. Guided Practice
Find the value of the variable. 6.
x = about 253.7
ANSWER

15. Lesson Quiz
Line t is tangent to the circle. Find the value of x and y. 1.
ANSWER
115

16. Lesson Quiz
Line t is tangent to the circle. Find the value of x and y. 2.
ANSWER 52

17. Lesson Quiz
Line t is tangent to the circle. Find the value of x and y. 3.
ANSWER 25

18. Lesson Quiz
Line t is tangent to the circle. Find the value of x and y. 4.
ANSWER
x = 81, y = 40.5