Write the other two angles of a right-angled isosceles triangle.

In the right-angled isosceles triangle ABC, ∠B = 90°

now we know that some of the angles of a triangle is $180°$

hence, $\angle A+\angle B+\angle C=180°$
or, ∠A + ∠C = 180° – 90° = 90°
But here given that,  ∠A = ∠B

then,
∠A = ∠C =$\frac{90°}{2}=45°$

Hence the required angles are ∠A = ∠C = 45°

hence, option D is the correct answer.