Question

In quadrilateral ABCD, AP and BP are bisectors of ∠A and ∠B respectively. Find the value of x, if D = 130º, ∠C = 60º.​

Answer 1

Answer:

[tex]AP and BP are bisectors of two adjacent angles A and B of a quadrilateral ABCD.

We know that the sum of all the angles of a quadrilateral is 360°. 

⇒∠A+∠B+∠C+∠D=360°,  ∠A+∠B=360°−(∠D+∠C)

∴ In △PAB;

⇒∠APB+∠PAB+∠PBA=180°    [ Angle sum property ]

⇒∠APB+21∠A+21∠B=180°

∴AP and BP are the bisectors of two adjacent angles A and B.

∴2∠APB+∠A+∠B=360°

⇒2∠APB=360°−(∠A+∠B)

∴2∠APB=∠C+∠D

⇒∠APB=2130o+60o=95°

∴x=95°.

Hence, the answer is 95°.