Consider the diagram in the picture provided. What is the measure of arc PD?(A) 35 degrees(B) 90 degrees(C) 110 degrees(D) 180 degrees

Accepted Solution

Answer:Option C. 110 degreesStep-by-step explanation:In this problem I assume that FD is a diametersoarc FP+arc PD=180° ----> because the diameter divide the circle into two equal partsstep 1Find the measure of arc FPwe know thatThe inscribed angle is half that of the arc it comprises.m<FEP=35°m<FEP=(1/2)(arc FP)substitute the values35°=(1/2)(arc FP)arc FP=70°step 2Find the measure of arc PDarc FP+arc PD=180° 70°+arc PD=180° arc PD=180°- 70°=110°