In △ABC, AB = AC, ∠A = (5x + 20)° and each of the base angle is $\dfrac{2}{5}$th of ∠A. Find the measure of ∠A.

Given, each of the base angle is $\dfrac{2}{5}$th of ∠A.

∴ Each base angle = $\dfrac{2}{5}$ × (5x + 20) = (2x + 8)°

In △ABC,

∠A + ∠B + ∠C = 180°

(5x + 20)° + (2x + 8)° + (2x + 8)° = 180°

9x° + 36° = 180°

9x° = 144°

x° = 16°.

(5x + 20)° = 5(16°) + 20° = 80° + 20° = 100°.

Hence, ∠A = 100°.