Points P, E, and A are marked on a circle whose center is R. In quadrilateral PEAR, angles A and E are found to be 54 degrees and 113 degrees, repectively.

Question

What are the other two angles?

Answer 1

Angles P and R are 59º and 134º, respectively. Angle PEA intercepts arc PA, so the measure of arc PA is 2(113º) = 226º. The minor arc PEA is then 360º - 226º = 134º. So angle R in quad PEAR, the same as central angle PRA, has measure 134º. Since the sum of the interior angles of a convex quadrilateral is 360º, angle P has measure 360º - 134º - 54º - 113º = 59º.