One angle of an isosceles triangle is 60°. What are the other two angles?

Let in Δ ABC,

∠A = 60°

It is given that triangle is a isosceles triangle.

Case 1

Two equal angles both equal to 60°

If it happens, then sum of two equal angles will be = 60 + 60 = 120°

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

Thus, the third angle = 180-120 = 60

Hence, other two angles are 60° each.

Case 2

Two equal angles other than given angle (∠A)

If ∠A = 60°

Let ∠B = ∠C = y°

Sum of all angles of a triangle is 180°

∴ ∠A + ∠B + ∠C = 180°

60 + y + y = 180°

60 + 2y = 180°

2y = 180-60

= 120

∴

Hence the other 2 angles are also 60°

Hence, in both the cases the triangle is equilateral (each angle = 60°)