Question

4. The bisectors of ZA and ZB of quadrilateral
ABCD meet at P. If ZC = 110° and ZD = 50°,
find ZAPB.
50°
Р
110°
A
B​

Answer 1

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 (210o) = 180° – 105° = 75° ∴ The measure of ∠APB