Here given triangle is isosceles right angled triangle.

So let our triangle be ∆ABC, right angled at A.

∴ ∠A = 90°

Here, AB = AC, as our given triangle is isosceles triangle.

Hence, base angles, ∠B and ∠C are equal.

Also, We know that,

Sum of all angles in any triangle = 180°

∴ ∠A + ∠B + ∠C = 180°

90° + 2 ∠B = 180°

2∠B = 90°

∠B = 45°

Hence the measure of each of the equal angles of a right-angled isosceles triangle is 45°