Question

The bisectors of ∠A and ∠B of quadrilateral ABCD meet at P. If ∠C = 96˚ and ∠D =
30˚, find the measure of ∠APB.

Answer 1

Step-by-step explanation:

60

∘

+100

∘

+∠A+∠B=360

∘

⇒∠A+∠B=200

∘

⇒

2

∠A+∠B

=100

∘

⇒∠BAP+∠ABP=100

∘

But ∠BAP+∠ABP+∠APB=180

∘

⇒∠APB=80

∘

Answer 2

Solution

We know that ,

Sum of angles of a quadrilateral is =360°

In the quadrilateral ABCD,

Given :∠C =96, ∠D = 100°

∠A + ∠B + ∠C + ∠D = 360°

∠A + ∠B + 96° +100°=360°

∠A + ∠B = 360° – 196°

∠A + ∠B = 164° ……. (Equation 1)

Now in triangle APB,

1/2 (∠A + ∠B) + ∠APB = 180° (since, sum of triangle is 180°)

∠APB = 180° – ½ (∠A + ∠B)…(Equation 2)

On substituting value of ∠A + ∠B = 164°  from equation (1) in equation (2) ,

∠APB = 180° – ½ (164° )

= 180° – 82° = 98°

∴ The measure of ∠APB is 98°.

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Hope it will help you