In ∆ABC, ∠A = 50°, ∠B = 70° and bisector of ∠C meets AB in D (Fig. 6.17). Measure of ∠ADC is.

Given: ∠A = 50°, ∠B = 70° and bisector of ∠C meets AB in D

Formula Used/Theory:-

Angle Sum property

Sum of angles of triangle is 180°

In Δ ABC

∠A + ∠B + ∠C = 180°

50° + 70° + ∠C = 180°

∠C = 180° - 120° = 60°

If CD is bisector of ∠C

Then;

∠DCA = ∠DCB = = 30°

In Δ ADC

∠A + ∠DCA + ∠ADC = 180°

50° + 30° + ∠ADC = 180°

∠ADC = 180° - 80° = 100°