In ΔABC, ∠B = 60° and ∠C = 40°. If AD and AE be respectively the internal bisector of ∠A and perpendicular on BC, then the measure of ∠DAE is

Answer: Option B

According to question,

Given :
∠B = 60°
∠C = 40°
As we know that
∠A + ∠B + ∠C = 180°
∠A = 180° - 60° - 40°
∠A = 80°
∴ ∠BAD = $$\frac{{80}^{\circ }}{2}$$ = 40°
In ΔAEB
∠A + ∠B + ∠E = 180°
∠A = 180° - 60° - 90°
∠A = 30°
Then,
∠DAE = ∠DAB - ∠EAB
∠DAE = 40° - 30°
∠DAE = 10°

---

By Trick
$$\begin{array}{rl}& \angle DAE=\frac{\angle B-\angle C}{2}\\ & =\frac{{60}^{\circ }-{40}^{\circ }}{2}\\ & =10^{\circ }\end{array}$$