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°
