Question

In Fig. 2.23, ABC is an equilateral triangle. P is a point on AC such that PBC = 46°. Calculate APB. B 46° A P C​

Answer 1

Since ABC is an equilateral triangle, all of its interior angles are equal to 60°. Therefore, ∠BAC = 60°.

Since ∠PBC = 46°, ∠ABC = 60° - 46° = 14°.

Since ∠ABC = 14°, ∠ACB = 60° - 14° = 46°.

Therefore, ∠APB = 180° - ∠BAC - ∠ACB = 180° - 60° - 46° = 74°.

The answer is 74°.