Question

In quadrilateral ABCD ,AP and BP are bisectors of <A and <B respectively.Then find <APB if C=60 and D=130 I need the ans​

Answer 1

Answer:

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