1. Warm-Up Exercises ANSWER 58 ANSWER 120 2.x = ( 360 – 120) = 0 1212 1.2x = 84 + 32 Solve for x.

2. Warm-Up Exercises ANSWER 82 3. 180 – x = (( 2x + 4) + 28). 1212 4. One-half of the measure of an angle plus its supplement is equal to the measure of the angle. Find the measure of the angle. Solve for x. ANSWER 45º

3. Warm-Up Exercises EXAMPLE 1 Find angle and arc measures Line m is tangent to the circle. Find the measure of the red angle or arc. SOLUTION = 1212 (130 o ) = 65 o = 2 (125 o ) = 250 o b.m KJL a.m 1

4. Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. SOLUTION = 1212 (210 o ) = 105 o m 1

5. Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. = 2 (98 o ) = 196 o m RST SOLUTION

6. Warm-Up Exercises GUIDED PRACTICE for Example 1 Find the indicated measure. = 2 (80 o ) = 160 o m XY SOLUTION

7. Warm-Up Exercises EXAMPLE 2 Find an angle measure inside a circle Find the value of x. SOLUTION The chords JL and KM intersect inside the circle. Use Theorem 10.12. xoxo = 1212 (mJM + mLK) xoxo = 1212 (130 o + 156 o ) Substitute. xoxo = 143 Simplify.

8. Warm-Up Exercises EXAMPLE 3 Find an angle measure outside a circle Find the value of x. SOLUTION Use Theorem 10.13. Substitute. Simplify. The tangent CD and the secant CB intersect outside the circle. = 1212 (178 o – 76 o ) xoxo = 51 x m BCD (mAD – mBD) = 1212

9. Warm-Up Exercises EXAMPLE 4 Solve a real-world problem 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.)

10. Warm-Up Exercises EXAMPLE 4 Solve a real-world problem SOLUTION Use Theorem 10.13. Substitute. 149 o 1212 [(360 o – x o ) –x o ] Solve for x. xoxo 31 = 1212 m BCD (mDEB – mBD) 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°. ANSWER The measure of the arc from which the flash is visible is about 31 o.

11. Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 4. Find the value of the variable. y = 61 o ANSWER

12. Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 Find the value of the variable. 5.5. = 104 o a ANSWER

13. Warm-Up Exercises GUIDED PRACTICE for Examples 2, 3, and 4 6. Find the value of the variable. xoxo 253.7 o ANSWER

14. Warm-Up Exercises Daily Homework Quiz ANSWER 115 1. Line t is tangent to the circle. Find the value of x and y.

15. Warm-Up Exercises Daily Homework Quiz 2. Line t is tangent to the circle. Find the value of x and y. ANSWER 52

16. Warm-Up Exercises Daily Homework Quiz 3. Line t is tangent to the circle. Find the value of x and y. ANSWER 25

17. Warm-Up Exercises Daily Homework Quiz 4. Line t is tangent to the circle. Find the value of x and y. ANSWER x = 81; y = 40.5