Q. 44.2( 24 Votes )

# 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.

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