In Fig. 16.21, the bisectors of ∠ A and ∠ B meet at a point P . If ∠ C =100° and ∠ D = 50°, find the measure of ∠ APB .

Question

In Fig. 16.21, the bisectors of &#x2220; A and &#x2220; B meet at a point P . If &#x2220; C =100&#xB0; and &#x2220; D = 50&#xB0;, find the measure of &#x2220; APB .

Philoid · Accepted Answer

Sum of angles of a quadrilateral is 360°

In the quadrilateral ABCD

∠D = 50°, ∠C = 100°,

∠A + ∠B + ∠C + ∠D = 360°

∠A + ∠B + 100° + 50° =

∠A + ∠B =

∠A + ∠B = 210° ……….(i)

Now in Δ APB

[Sum of angles of a triangle is 180°]

…….(ii)

On substituting value of ∠A + ∠B = 210 from equation (i) in equation (ii)

In Fig. 16.21, the bisectors of ∠A and ∠B meet at a point P. If ∠C =100° and ∠D = 50°, find the measure of ∠APB.