9514 1404 393
Answer:
∠Q = 89°
∠R = 123°
∠S = 91°
Explanation:
It seems easiest to start by finding the measures of each of the arcs. The measure of an arc is double the measure of the inscribed angle it subtends.
arc QRS = 2·∠P = 114°
So, ...
arc QR = arc QRS - arc RS = 114° -41° = 73°
The total of the arcs around the circle is 360°, so ...
arc PQ = 360° -arc PS -arc QRS
arc PQ = 360° -137° -114° = 109°
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∠Q = (1/2)(arc RS + arc PS) = (1/2)(41° +137°)
∠Q = 89°
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∠R = (1/2)(arc PS +arc PQ) = (1/2)(137° +109°)
∠R = 123°
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∠S = (1/2)(arc PQ +arc QR) = (1/2)(109° +73°)
∠S = 91°