Question

ABCD is a quadrilateral in which measures of angle D and angle C are 60 degrees, and 100 degrees respectively. If the internal bisectors of angle A and angle B meet at P, then measure of angle APB is

Options

• 80°

• 90°

• 100°

• 110°

Answer 1

80°

Explanation:

Let ∠BAD = 2x and ∠ABC = 2y.

then, in quadrilateral ABCD,

∠(A + B +C +D) = 360°

2x+ 2y +100° + 60° = 360°

2 (x + y) = 200°

∴ (x + y) = 100°  .............(i)

As, AP and BP are angle bisector of ∠A and ∠B respectively

Then, ∠BAP = x and ∠ABP = y.

Again in ΔAPB, the sum of angles 180°