In Figure, the bisectors of ∠A and ∠B meet at a point P. If

1.	In Figure, the bisectors of ∠A and ∠B meet at a point P. If ∠C =100° and ∠D = 50°, find the measure of ∠APB.
Answer» 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 (210^o) = 180° – 105° = 75° ∴ The measure of ∠APB is 75°

In Figure, the bisectors of ∠A and ∠B meet at a point P. If ∠C =100° and ∠D = 50°, find the measure of ∠APB.

Answer»

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 (210^o)

= 180° – 105°

= 75°

∴ The measure of ∠APB is 75°