Question

one angle of an isosceles triangle measures 46°. what measures are possible for the other two angles? choose all that apply. 67° 70° 46° 88°

Explanation:

Step1: Consider the given angle as a base - angle

In an isosceles triangle, if the given $46^{\circ}$ angle is a base - angle, then the other base - angle is also $46^{\circ}$. Using the fact that the sum of the interior angles of a triangle is $180^{\circ}$, the third angle is $180-(46 + 46)=88^{\circ}$.

Step2: Consider the given angle as the vertex - angle

If the $46^{\circ}$ angle is the vertex - angle, then the sum of the two base - angles is $180 - 46=134^{\circ}$. Since the base - angles of an isosceles triangle are equal, each base - angle is $\frac{134}{2}=67^{\circ}$.

Answer:

A. $67^{\circ}$, C. $46^{\circ}$, D. $88^{\circ}$