Question

In the adjacent figure,the bisectors of ∠A and ∠B meet in a point p. If ∠C = 100° and ∠D = 60° , find the measure of ∠APB. please solve this.

Answer 1

In quadrilateral ABCD, AP and BP are the biscetors of A and B then APB=1/2 C+D.Itz a theorem

Therefore, 100+60÷2=80

Answer 2

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!

Please mark this as the best answer