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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.
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Solution
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.
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