Question

abcd is a parallelogram angle a = 120 if the bisectors of angle a and b meet at a point p show that angle apb = 90​

Answer 1

Step-by-step explanation:

∠A+∠B = 180°. ( adjacent sides of llgm)

120° +∠B = 180°

∠B= 180°- 120°

= 60°

∠pab = ∠dap (ap is a bisector of ∠a)

= 1/2 ∠A

= 60°

∠pba= ∠cbp (bp is a bisector of ∠b)

=1/2 ∠B

= 30°

In ▲ APB

∠apb +∠pba +∠pab = 180° (angle sum property of ▲)

∠apb + 60°+30° = 180°

∠apb = 180° - (60°+30°)

∠apb = 180° - 90°

∠apb = 90°

hence, proved

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