Question

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. 

Answer 1

\[∠A + ∠B + ∠C +∠D = 360° \]

\[ \Rightarrow ∠A +∠B + 100°+ 50° = 360° \]

\[ \Rightarrow ∠A + ∠B = 210° . . . (i)\]

\[\text{ In }  \bigtriangleup APB, \text{ we have } : \]

\[\frac{1}{2}∠A + \frac{1}{2}∠B + ∠APB = 180° \] 

\[ \Rightarrow ∠APB = 180° - \frac{1}{2}\left( ∠A + ∠B \right)\] 

\[\text{ From (i), we get: } \]

\[ \Rightarrow ∠APB = 180° - \left( \frac{1}{2} \times 210° \right) \]

\[ \therefore ∠APB = 75° \]