In the adjoining figure, ABCD is a quadrilateral such that ∠D + ∠C = 100°. The bisectors of ∠A and ∠B meet at ∠P. Determine ∠APB.

We know that the sum of the angles in a quadrilateral is 360⁰.

i.e, ∠A + ∠B + ∠C + ∠D = 360⁰. ...... (1)

We also know that the sum of angles in a triangle is 180⁰.

According to the problem, it is given that ∠C + ∠D = 100⁰.

Substituting the condition in the eq(1) we get,

⇒ ∠A + ∠B + 100⁰ = 360⁰

⇒ ∠A + ∠B = 360⁰ - 100⁰

⇒ ∠A + ∠B = 260⁰.

⇒

⇒ . ...... (2)

According to the problem, it is given that the ΔABP is formed by the intersection of angular bisectors of ∠A and ∠B.

From ΔABP, We can write that,

⇒

⇒ 130⁰ + ∠P = 180⁰ (From eq(2))

⇒ ∠P = 180⁰ - 130⁰

⇒ ∠ P = 50⁰.

The value of the ∠P is 50⁰.