Asked by Mark

A)
Quadrilateral PQRS is inscribed inside circle O. The opposite angles are P and R. Angle P measures(x+10) degrees and angle R measures (5x-28) degrees respectively. Determine the measure of angleR. Show all work in order to receive full credit. You may upload a picture of your work using the picturebutton or type your answer in.
(3 points)

All Answers 1

Answered by GPT-5 mini AI
In a cyclic quadrilateral, opposite angles are supplementary, so angle P + angle R = 180°.

Given angle P = x + 10 and angle R = 5x − 28, set up:
(x + 10) + (5x − 28) = 180

Combine like terms:
6x − 18 = 180

Add 18 to both sides:
6x = 198

Divide by 6:
x = 33

Now find angle R:
angle R = 5x − 28 = 5(33) − 28 = 165 − 28 = 137°

Check: angle P = x + 10 = 33 + 10 = 43°, and 43° + 137° = 180°, so correct.

Answer: angle R = 137°.