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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.
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Solution
\[∠A + ∠B + ∠C +∠D = 360° \]
\[ \Rightarrow ∠A +∠B + 100°+ 50° = 360° \]
\[ \Rightarrow ∠A + ∠B = 210° . . . (i)\]
\[\text{ In } \bigtriangleup APB, \text{ we have } : \]
\[\frac{1}{2}∠A + \frac{1}{2}∠B + ∠APB = 180° \]
\[ \Rightarrow ∠APB = 180° - \frac{1}{2}\left( ∠A + ∠B \right)\]
\[\text{ From (i), we get: } \]
\[ \Rightarrow ∠APB = 180° - \left( \frac{1}{2} \times 210° \right) \]
\[ \therefore ∠APB = 75° \]
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