Question

Abcd is a parallelogram in which angle b is 120 degree and the bisector of angle a and angle b meet at p. Prove that angle apb is a right angle

Answer 1

first ans is the property of parallelogram is as follows
diagonals of parallelogram is perpendicular bisecter.
here, angle APB= 90°

secondly,
angle A+angle B= 180° .....adjacent angles in parallelogram is 180°
angle A+120=180
angleA=180-120
angle A = 60°
therefore
angle PAB = 60°......angle bisecter theorem
angle PBA= 60°....angle bisecter theorem
in ∆ABP,
angle PAB+ angleABP+ angleAPB= 180°
30°+60°+angleAPB=180°
angle APB = 180-90 =90°.