example 1 use inscribed angles a. m t mqrb. find the indicated measure in p. solution 1 2 1 2 m t =...
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![Page 1: EXAMPLE 1 Use inscribed angles a. m T mQRb. Find the indicated measure in P. SOLUTION 1 2 1 2 M T = mRS = (48 o ) = 24 o a. mQR = 180 o mTQ = 180 o 100](https://reader036.vdocument.in/reader036/viewer/2022081821/56649e725503460f94b709a9/html5/thumbnails/1.jpg)
EXAMPLE 1 Use inscribed angles
a. m T mQRb.
Find the indicated measure in P.
SOLUTION
12
12
M T = mRS = (48o) = 24oa.
mQR = 180o mTQ = 180o 100o = 80o. So, mQR = 80o. – –
mTQ = 2m R = 2 50o = 100o. Because TQR is a semicircle,b.
![Page 2: EXAMPLE 1 Use inscribed angles a. m T mQRb. Find the indicated measure in P. SOLUTION 1 2 1 2 M T = mRS = (48 o ) = 24 o a. mQR = 180 o mTQ = 180 o 100](https://reader036.vdocument.in/reader036/viewer/2022081821/56649e725503460f94b709a9/html5/thumbnails/2.jpg)
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.12
12
![Page 3: EXAMPLE 1 Use inscribed angles a. m T mQRb. Find the indicated measure in P. SOLUTION 1 2 1 2 M T = mRS = (48 o ) = 24 o a. mQR = 180 o mTQ = 180 o 100](https://reader036.vdocument.in/reader036/viewer/2022081821/56649e725503460f94b709a9/html5/thumbnails/3.jpg)
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.
![Page 4: EXAMPLE 1 Use inscribed angles a. m T mQRb. Find the indicated measure in P. SOLUTION 1 2 1 2 M T = mRS = (48 o ) = 24 o a. mQR = 180 o mTQ = 180 o 100](https://reader036.vdocument.in/reader036/viewer/2022081821/56649e725503460f94b709a9/html5/thumbnails/4.jpg)
GUIDED PRACTICE for Examples 1, 2 and 3
Find the measure of the red arc or angle.
1.
SOLUTION
12
12
M G = mHF = (90o) = 45oa.
![Page 5: EXAMPLE 1 Use inscribed angles a. m T mQRb. Find the indicated measure in P. SOLUTION 1 2 1 2 M T = mRS = (48 o ) = 24 o a. mQR = 180 o mTQ = 180 o 100](https://reader036.vdocument.in/reader036/viewer/2022081821/56649e725503460f94b709a9/html5/thumbnails/5.jpg)
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.
![Page 6: EXAMPLE 1 Use inscribed angles a. m T mQRb. Find the indicated measure in P. SOLUTION 1 2 1 2 M T = mRS = (48 o ) = 24 o a. mQR = 180 o mTQ = 180 o 100](https://reader036.vdocument.in/reader036/viewer/2022081821/56649e725503460f94b709a9/html5/thumbnails/6.jpg)
GUIDED PRACTICE for Examples 1, 2 and 3
Find the measure of the red arc or angle.
3.
SOLUTION
ZYN ZXN
ZXN 72°
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