The given figure, shows an isosceles triangle with angle ABC = 90°, the measure of angle BAC is :

1. 30°

2. 45°

3. 60°

4. 40°

Given that Δ ABC is isosceles, ∠ BAC = ∠ BCA.

Let ∠BAC = ∠BCA = x.

Using the angle sum property of a triangle, which states that the sum of all angles in a triangle is 180°:

⇒ ∠BAC + ∠BCA + ∠ABC = 180°

⇒ x + x + 90° = 180°

⇒ 2x + 90° = 180°

⇒ 2x = 180° - 90°

⇒ 2x = 90°

⇒ x = $\dfrac{90°}{2}$

⇒ x = 45°

Hence, ∠BAC = 45°.

Hence, option 2 is the correct option.