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 = 140/2

= 70 

∴ The measures of the angles ∠A and ∠B is 70° each.