EXAMPLE 1 Use inscribed angles Find the indicated measure in P. a. m T

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Presentation transcript:

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

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

EXAMPLE 3 Standardized Test Practice SOLUTION Notice that JKM and JLM intercept the same arc, and so JKM JLM by Theorem 10.8. Also, KJL and KML 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.

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

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

GUIDED PRACTICE for Examples 1, 2 and 3 Find the measure of the red arc or angle. 3. SOLUTION Notice that ZYN and ZXN intercept the same arc, and so ZYN by Theorem 10.8. Also, KJL and KML intercept the same arc, so they must also be congruent. ZXN ZYN ZXN ZXN 72°

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

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

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

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

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

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

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

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

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