Answer :

Applying the inscribed angle theorem, the measures of the angles and arcs in the image given are:

Arc QR = 48°

Arc RS = 96°

Arc QPS = 216°

Arc PSR = 186°

Arc SRQ = 144°

What is the Inscribed Angle Theorem?

The inscribed angle theorem state that the measure of an intercepted arc is equal to twice the measure of the inscribed angle.

Find arc PSR:

Arc PSR = 2(93) [based on the inscribed angle theorem]

Arc PSR = 186°

Find arc QR:

Arc QR = 360 - arc PQ - arc PSR

Substitute

Arc QR = 360 - 126 - 186

Arc QR = 48°

Arc RS = arc PSR - arc PS

Arc RS = 186 - 90

Arc RS = 96°

Arc QPS = 126 + 90

Arc QPS = 216°

Arc PSR = arc PS + arc RS

Arc PSR = 90 + 96

Arc PSR = 186°

Arc SRQ = arc RS + arc QR

Arc SRQ = 96 + 48

Arc SRQ = 144°

Learn more about the inscribed angle theorem on:

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Answer: 48 96

Step-by-step explanation:

Arc QR = 360 - 126 - 186

Arc QR = 48°

Arc RS = arc PSR - arc PS

Arc RS = 186 - 90

Arc RS = 96°