One angle of an isosceles triangle measures 120°. What measures are possible for the other two angles?

In an isosceles triangle, two angles are the same, and the sum of all angles in a triangle is always 180°.

Given that one angle measures 120°, the other two angles must add up to:

180° – 120° = 60°.

Since the two other angles are equal in an isosceles triangle, we divide the remaining 60° by 2:

60° ÷ 2 = 30°.

Thus, the measures for the other two angles are both 30°.

The possible measure for the other two angles is:

30°.

The other options (40°, 20°, and 120°) are not valid because they do not satisfy the angle sum property of a triangle.

In an isosceles triangle, two angles are the same, and the sum of the angles in any triangle is always 180°. If one angle measures 120°, the other two angles must be equal, as they are the base angles of the isosceles triangle.

Let’s denote the two equal angles as ( x ). Thus, we can set up the equation:

[ 120° + 2x = 180° ]

Now, solving for ( x ):

1. Subtract 120° from both sides:

[ 2x = 60° ]

2. Divide by 2:

[ x = 30° ]

Therefore, the measures of the other two angles must be 30° each.

The possible measures for the other two angles are 30°.

So, from the provided options, only 30° is correct.

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