In ΔABC, ∠B = 70° and ∠C = 30°, AD and AE are respectively the perpendicular on side BC and bisector of ∠A. The measure of ∠DAE is:

A. 24°

B. 10°

C. 15°

D. 20°

Answer: Option D

Solution(By Examveda Team)

∠A = 180° - (∠B + ∠C)
∠A = 180° - 100°
∠A = 80°
∠BAE = ∠EAC = $$\frac{1}{2}$$ ∠A = 40°
In ΔBAD
∠BAD = 90° - ∠B
∠BAD = 90° - 70°
∠BAD = 20°
∠DAE = ∠BAE - ∠BAD
∠DAE = 40° - 20°
∠DAE = 20°