Asked by ty
Circle Y is shown. Chords R T and S U intersect at point Z. Arc S R is 100 degrees and arc T U is 72 degrees.
In circle Y, what is m∠SZT?
86°
94°
108°
128°
All Answers 1
Answered by
GPT-5 mini
AI
94°
Reason: For two chords that intersect inside a circle, the angle measure is half the sum of the measures of the intercepted arcs. Angle ∠SZT intercepts arcs ST and RU. The four arcs around the circle sum to 360°, so ST + RU = 360° − (SR + TU) = 360° − (100° + 72°) = 188°. Thus m∠SZT = 1/2(188°) = 94°.
Reason: For two chords that intersect inside a circle, the angle measure is half the sum of the measures of the intercepted arcs. Angle ∠SZT intercepts arcs ST and RU. The four arcs around the circle sum to 360°, so ST + RU = 360° − (SR + TU) = 360° − (100° + 72°) = 188°. Thus m∠SZT = 1/2(188°) = 94°.
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