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

2. 3.180 – x = ((2x + 4) + 28) 1 2 1 2 82 58 ANSWER ANSWER 2. x = ( 360 – 120) = 0 120 ANSWER Warm-Up Solve for x. 1. 2x = 84 + 32

3. 120 ANSWER 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.

4. = a. m1 12 (130o) (125o) 2 = b. m KJL Example 1 Line mis tangent to the circle. Find the measure of the red angle or arc. SOLUTION = 65o = 250o

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

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

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

8. The chords JLand KMintersect inside the circle. (mJM + mLK) x° = 12 12 x° (130° + 156°) = x = 143 Example 2 Find the value of x. SOLUTION Use Theorem 10.12. Substitute. Simplify.

9. The tangent CDand the secant CBintersect outside the circle. (mAD – mBD) m BCD = 12 12 x° (178° – 76°) = x = 51 Example 3 Find the value of x. SOLUTION Use Theorem 10.13. Substitute. Simplify.

10. Example 4 SCIENCE 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.)

11. Because CBand CDare tangents, Also, BC DC and CA CA . So, ABC ADC by the Hypotenuse-Leg Congruence Theorem, and BCA DCA.Solve rightCBA to find thatm BCA 74.5°. (mDEB – mBD) m BCD = CB AB and CD AD 12 12 149° [(360° – x°) –x°] x 31 Example 4 SOLUTION Use Theorem 10.13. Substitute. Solve for x. The measure of the arc from which the flash is visible is about 31°.

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

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

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

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

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

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

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