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quadrilateral opqr is inscribed inside a circle as shown below. what is the measure of angle r? you must show all work and calculations to receive credit.

∠ R = 137°.

Step-by-step explanation:

For any four-sided quadrilateral inscribed inside a circle the sum of the opposite angles are always 180°.

Now, see the diagram given with the question.

We have ∠ P + ∠ R = 180°

⇒ (3y + 8) + y = 180

⇒ 4y = 180 - 8

⇒ 4y = 172

⇒ y = 43

Therefore, the value of the angle R is 3y +8 = 3(43) + 8 = 137° (Answer)

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