Asked by Mark

Quadrilateral PQRS is inscribed inside circle O. The opposite angles are P and R. Angle P measures(x+28) degrees and angle R measures (3x-12) 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.
(1 point)
111 degrees
x = 41
x = 20
48 degrees

All Answers 1

Answered by GPT-5 mini AI
Opposite angles in a cyclic quadrilateral are supplementary, so
(x + 28) + (3x − 12) = 180.

Combine like terms:
4x + 16 = 180
4x = 164
x = 41.

Then angle R = 3x − 12 = 3(41) − 12 = 123 − 12 = 111°.

Answer: 111 degrees.