ABC is a right angled isosceles triangle in which ∠A = 90°. If D and E are the mid-points of AB and AC respectively, then ∠ADE =

1. 30°

2. 45°

3. 60°

4. 90°

Given,

ABC is a right angled isosceles triangle. Since, hypotenuse is the largest side thus other two sides of triangle will be equal.

AC = AB

⇒ ∠C = ∠B = x (let)

In △ABC,

⇒ ∠A + ∠B + ∠C = 180°

⇒ 90° + x + x = 180°

⇒ 2x = 180° - 90°

⇒ 2x = 90°

⇒ x = $\dfrac{90°}{2}$

⇒ x = 45°

⇒ ∠C = ∠B = 45°

By mid-point theorem,

The line segment joining the mid points of any two sides of a triangle is parallel to the third side and is equal to half of it.

Since, D and E are the mid-points of AB and AC respectively.

DE || BC

AB is the transversal.

⇒ ∠ABC = ∠ADE (Corresponding angles are equal)

⇒ ∠ADE = 45°.

Hence, option 2 is the correct option.