Question

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

Answer 1

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Answer 2

Angle C = 100°

Angle D = 50°

Angle C + Angle B = 180°

100° + B = 180°

B = 180° - 100°

B = 80°

Angle ABP = 80/2 = 40°

Angle D + Angle A = 180°

50° + A = 180°

A = 180° - 50°

A = 130°

Angle BAP = 130/2 = 65°

Angle APB = x°

Sum of angles of triangle = 180°

65° + 40° + x° = 180°

105° + x° = 180°

x° = 180° - 105°

x° = 75°

therefore, the measure of angle APB = 75°

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