Question

in the given figure the bisector of angle A and Angle B meet at a point p. if angle C=100°and angleD=50°, find the measure of angle APB​

Answer 1

In quadilateral ABCD,LET angle PAB=PAD=x,angle PBA=PBC=y;

angle A+angle B+angle C+angle D=360

angle PAD +angle PAB +angle PBA +angle PBC+angle C+angle D=360

x+x+y+y+100+60=360

2(x+y)+160=360

2(x+y)=360-160

2(x+y)=200

x+y=200/2

x+y=100

Now in triangle PAB;

angle PAB+angle PBA+angle APB=180

x+y+ angle P=180

100+angle P=180 (Since x+y=100)

angle P=180-100

angle P=80

Hope I Helped!