Question

in the adjoining figure ABCD is a quadrilateral such that angle D + angle C is equal 200 degree the bisector of angle A and Angle B meet angle p.
determine angle APB .

Answer 1

angle A + angle B+angleC+ angle D=360
angleC+angle D=200 (given)
angleA+angleB+200=360
angleA+angleB=160

ATQ,
angleA/2+angleB/2=160/2
angleA/2+angleB/2=80..............(i)

now in triangle APB
anglePAB+anglePBA+angleAPB=180
80+angleAPB=180 (from i)
angleAPB=180-80
angleAPB=100