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EXAMPLE 1

Find the indicated measure in P. a. m T. b. mQR. a. M T = mRS = (48 o ) = 24 o. mTQ = 2 m R = 2 50 o = 100 o . Because TQR is a semicircle,. b. mQR = 180 o mTQ = 180 o 100 o = 80 o . So, mQR = 80 o. –. –. 1. 1. 2. 2. EXAMPLE 1.

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EXAMPLE 1

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  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

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