in circle y, what is m∠szt? 86° 94° 108° 128°
in circle y, what is m∠szt? 86° 94° 108° 128°
Answer
Answer:
108°
Explanation:
Step1: Recall angle - arc relationship
The measure of an inscribed angle is half the measure of its intercepted arc.
Step2: Find the measure of arc SU
The sum of the arcs of a circle is 360°. Given arc SR = 100° and arc TU=72°. Let arc SU be (x). Then (100 + x+72=360), so (x = 360-(100 + 72)=188).
Step3: Calculate (m\angle SZT)
(\angle SZT) is an inscribed angle that intercepts arc SU. By the inscribed - angle theorem, (m\angle SZT=\frac{1}{2}(m\overset{\frown}{SU})). Since (m\overset{\frown}{SU} = 216) (the non - minor arc SU, (360-(100 + 72)=188), and we use the non - minor arc here as the angle is a major inscribed angle), (m\angle SZT=\frac{1}{2}(216)=108^{\circ}).