In triangle ABC, ∠A : ∠B = 2 : 3 and ∠C exceeds ∠A by 40°. The bisector of ∠C meets AB at D. Find ∠ADC.

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Accepted Answer

100°. Let ∠A = 2k and ∠B = 3k, so ∠C = 2k + 40. Then 7k + 40 = 180, k = 20: ∠A = 40°, ∠B = 60°, ∠C = 80°. In triangle ADC, ∠ACD = 40°, so ∠ADC = 180° - 40° - 40° = 100°.

In triangle ABC, ∠A : ∠B = 2 : 3 and ∠C exceeds ∠A by 40°. The bisector of ∠C meets AB at D. Find ∠ADC.

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