Question

the bisector of angle A and angle B meet at a point P. If angle C=100° and angle D=60° ,find the measure of angle APB.

Answer 1

in this quadrilateral angles(a+b+c+d=360°) so,a+b=360°-(c+d)....1
in triangle abp
angle bap=a/2 because it is the bisector of angle a
angle abp=b/2 because it is a bisector of angle b
so, a/2+b/2+angle apb=180°  (Δs property).....2
now putting he value from 1 to 2
360°-(c+d)/2+angle apb=180°
360°/2+(-c-d/2)+angle apb=180°
180°+(-c-d/2)+angle apb=180°
angle apb=c+d/2
now putting the value of c and d
apb=100°+60°/2
apb=160°/2
apb=80°