One angle of an isosceles triangle is 90°. What are the other two angles?

Let in Δ ABC,

∠A = 90°

It is given that triangle is a isosceles triangle.

Case 1

Two equal angles both equal to 90°

If it happens, then sum of two equal angles will be = 90 + 90 = 180°

But, sum of all angles of a triangle is 180°

Thus, the third angle = 180-180 = 0

But, this is not possible.

Case 2

Two equal angles other than right angle.

If ∠A = 90°

Let ∠B = ∠C = y°

Sum of all angles of a triangle is 180°

∴ ∠A + ∠B + ∠C = 180°

90 + y + y = 180°

90 + 2y = 180°

2y = 180-90

= 90

∴

Hence the other 2 angles are 45°