Question

one angle of an isosceles triangle measures 120°. what measures are possible for the other two angles? choose all that apply. 30° 75° 40° 25°

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is $180^{\circ}$. In an isosceles triangle, two angles are equal.

Step2: Analyze the given angle

The given angle of $120^{\circ}$ cannot be one of the equal - angles because if there were two $120^{\circ}$ angles, the sum of those two angles alone would be $120^{\circ}+120^{\circ}=240^{\circ}>180^{\circ}$.

Step3: Calculate the equal angles

Let the measure of each of the equal angles be $x$. Then, using the angle - sum property of a triangle, we have $120^{\circ}+x + x=180^{\circ}$. Combining like terms gives $120^{\circ}+2x = 180^{\circ}$. Subtract $120^{\circ}$ from both sides: $2x=180^{\circ}-120^{\circ}=60^{\circ}$. Divide both sides by 2: $x = 30^{\circ}$.

Answer:

A. $30^{\circ}$