Question

In figure 2, the bisectors of angle A and B meets at point P. If angle C =50° and D =100°, find the measure of angle APB.

Answer 1

let angle DAP=BAP=x °

let angle CBP=PBA=y°

By angle sum property of a quadrilateral,

2x+2y+100°+50°=360°

2(x+y)=210°

x+y=105°

By angle sum property in traingle APB,

x+y+angle APB=180°

Angle APB=180°-105°

=75°