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

Ans:

We know that Sum of angles of a quadrilateral is = 360°

In the quadrilateral ABCD  

Given, ∠C =100° and ∠D = 50°

∠A + ∠B + ∠C + ∠D = 360°

∠A + ∠B + 100° + 50° = 360°

∠A + ∠B = 360° – 150°

∠A + ∠B = 210° ……. (Equation 1)

Now in Δ APB

½ ∠A + ½ ∠B + ∠APB = 180° (since, sum of triangle is 180°)

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

On substituting value of ∠A + ∠B = 210 from equation (1) in equation (2)

∠APB = 180° – ½ (210o)

= 180° – 105°

= 75°

∴ The measure of ∠APB is 75°

Answer 2

Answer:

Step-by-step explanation:

We know, the sum all angles in a quadrilateral is 360°

So In the quadrilateral ABCD,

∠A + ∠B + ∠C + ∠D = 360°

∠A + ∠B + 96° + 30° = 360°

∠A + ∠B + 126° = 360°

∠A + ∠B = 360 - 126

∠A + ∠B = 234°            _ ( name as equation 1 )

Now, In the Δ APB ,

1/2∠A + 1/2∠B + ∠APB = 180     _ ( Sum of all angles in a triangles is 180°)

1/2 (∠A + ∠B) + ∠APB = 180°

1/2 X 234 + ∠APB = 180°

117 + ∠APB = 180°

∠APB = 180 - 117

∠APB = 63°

HENCE, the measure of ∠APB is 63°

WELL !! I HOPE IT HELPED,

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