Question

hi
the bisector of LA and LB meet at a point P . If LC=50° and LD=100° Find the measure of LAPB​​​

Answer 1

75°

Step-by-step explanation:

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°