The side BC of ΔABC is produced to D. If ∠ACD = 108° and ∠B = ∠A/2, then ∠A is
Solution
We know that the exterior angle is equal to the sum of opposite interior angles. ∠ACD = ∠ABC + ∠BAC Given, ∠B = $$\frac{\angle A} {2}$$ 108° = $$\frac{\angle A} {2}$$ + ∠A ∠A = (108 × 2)/3 = 72°.