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3 years ago

M∠Q = m∠R = m∠S = 40 POINTS!!!!!!!

Mathematics

1 answer:

Marizza181 [45]3 years ago

7 0

9514 1404 393

Answer:

∠Q = 89°

∠R = 123°

∠S = 91°

Step-by-step 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°

∠Q = (1/2)(arc RS + arc PS) = (1/2)(41° +137°)

∠Q = 89°

∠R = (1/2)(arc PS +arc PQ) = (1/2)(137° +109°)

∠R = 123°

∠S = (1/2)(arc PQ +arc QR) = (1/2)(109° +73°)

∠S = 91°

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Solnce55 [7]

Hey, there!!

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Dont forget to make this the brainliest answer to help those in need. also add a 5 star and a heart. thanks for the support hope it helped. have a nice day

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