Question

∠ACD is an exterior angle of ∆ABC. The measures of ∠A and ∠B are equal. If m∠ACD = 140^°, find the measures of the angles ∠A and ∠B. 

Answer 1

Let the measures of ∠A be x^°.

m∠A = m∠B = x^°

∠ACD is the exterior angle of ∆ABC

∴ m∠ACD = m∠A + m∠B

∴ 140^° = x + x

∴ 140^° = 2x

∴ 2x = 140^°

∴ x = `140^circ/2`

= 70^°

∴ The measures of the angles ∠A and ∠B are 70^°, respectively.