1. 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 = o = 100o. Because TQR is a semicircle, b.
mQR = 180o mTQ = 180o 100o = 80o. So, mQR = 80o. –

2. 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

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

4. 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 Also, KJL and KML intercept the same arc, so they must also be congruent.
ZXN
ZYN
ZXN
ZXN
72°