Problem 176

The sum of the three angles in any triangle is $180^{\circ}$.

If one of the angles in an isosceles triangle measures $50^{\circ}$, then the sum of the measures of the two unknown angles in the triangle is $180^{\circ}-50^{\circ}=130^{\circ}$.

Since the triangle is isosceles, then two of the angles in the triangle have equal measure.

If the two unknown angles are equal in measure, then they each measure $130^{\circ}\div2=65^{\circ}$.

However, $65^{\circ}$ and $65^{\circ}$ is not one of the given answers.

If the measure of one of the unknown angles is equal to the measure of the given angle, $50^{\circ}$, then the third angle in the triangle measures $180^{\circ}-50^{\circ}-50^{\circ}=80^{\circ}$.

Therefore, the measures of the other angles in this triangle could be $50^{\circ}$ and $80^{\circ}$.