ANSWER

1. 25 ANSWER 60º; 120º ANSWER 1.The measure of the interior angles of a quadrilateralare 80º, 100º, 55º, and 5xº. Find the value of x. 2.Two supplementary angles have measures 6xº and12xº. Find each angle measure.

2. 3.Solve 3x = ( 4x + 12). 1 2 1 2 6 ANSWER 4. Solve 80 = ( 360 – 2x). 100 ANSWER

3. Find the indicated measure inP. a. mT b. mQR a. M T = mRS = (48o) = 24o mTQ = 2m R = 2 50o = 100o. BecauseTQR is a semicircle, b. mQR = 180o mTQ = 180o 100o = 80o. So, mQR = 80o. – – 1 1 2 2 EXAMPLE 1 Use inscribed angles SOLUTION

4. Find mRSand mSTR. What do you notice about STRand RUS? From Theorem 10.7,you know thatmRS = 2m RUS= 2 (31o) = 62o. Also, m STR = mRS = (62o) = 31o. So,STR RUS. 1 1 2 2 EXAMPLE 2 Find the measure of an intercepted arc SOLUTION

5. Notice thatJKM andJLM intercept the same arc, and soJKM JLM by Theorem 10.8. Also, KJL andKML intercept the same arc, so they must also be congruent. Only choice C contains both pairs of angles. So, by Theorem 10.8, the correct answer is C. EXAMPLE 3 Standardized Test Practice SOLUTION

6. a. m G = mHF = (90o) = 45o 1 1 2 2 for Examples 1, 2 and 3 GUIDED PRACTICE Find the measure of the red arc or angle. 1. SOLUTION

7. mTV = 2m U = 2 38o = 76o. b. for Examples 1, 2 and 3 GUIDED PRACTICE Find the measure of the red arc or angle. 2. SOLUTION

8. Notice thatZYN andZXN intercept the same arc, and soZYN byTheorem 10.8. Also, KJL andKML intercept the same arc, so they must also be congruent. ZXN ZYN ZXN ZXN 72° for Examples 1, 2 and 3 GUIDED PRACTICE Find the measure of the red arc or angle. 3. SOLUTION

9. Your camera has a 90o field of vision and you want to photograph the front of a statue. You move to a spot where the statue is the only thing captured in your picture, as shown. You want to change your position. Where else can you stand so that the statue is perfectly framed in this way? EXAMPLE 4 Use a circumscribed circle Photography

10. From Theorem 10.9, you know that if a right triangle is inscribed in a circle, then the hypotenuse of the triangle is a diameter of the circle. So, draw the circle that has the front of the statue as a diameter. The statue fits perfectly within your camera’s 90o field of vision from any point on the semicircle in front of the statue. EXAMPLE 4 Use a circumscribed circle SOLUTION

11. for Example 4 GUIDED PRACTICE 4. What If ? In Example 4,explain how to find locations if you want to frame the front and left side of the statue in your picture. SOLUTION Make the diameter of your circle the diagonal of the rectangular base.

12. a. PQRS is inscribed in a circle, so opposite angles are supplementary. a. mQ + m S = 180o m P + m R = 180o EXAMPLE 5 Use Theorem 10.10 Find the value of each variable. SOLUTION 75o + yo = 180o 80o + xo = 180o y = 105 x = 100

13. b. JKLMis inscribed in a circle, so opposite angles are supplementary. b. mK + m M = 180o m J + m L = 180o EXAMPLE 5 Use Theorem 10.10 Find the value of each variable. SOLUTION 4bo + 2bo = 180o 2ao + 2ao = 180o 6b = 180 4a = 180 b = 30 a = 45

14. for Example 5 GUIDED PRACTICE Find the value of each variable. 5. SOLUTION y = 112 x = 98

15. for Example 5 GUIDED PRACTICE Find the value of each variable. 6. SOLUTION c = 62 x = 10

16. Find the value of x . 1. ANSWER 38 Daily Homework Quiz

17. ANSWER 56 Daily Homework Quiz Find the value of x . 2.

18. ANSWER 44 Daily Homework Quiz Find the value of x . 3.

19. ANSWER x = 54; y = 20 Daily Homework Quiz Find the value of each variable. 4.

20. ANSWER x = 5; y = 10 Daily Homework Quiz Find the value of each variable. 5.