Question

one angle of an isosceles triangle measures 68°. what measures are possible for the other two angles? choose all that apply. 56° 44° 57° 68°

Explanation:

Step1: Consider the given angle as a base - angle

If the given $68^{\circ}$ angle is a base - angle, then the other base - angle is also $68^{\circ}$.

Step2: Calculate the third angle

Let the third angle be $x$. Using the angle - sum property of a triangle ($x + 68^{\circ}+68^{\circ}=180^{\circ}$), we get $x = 180^{\circ}- 2\times68^{\circ}=180^{\circ}-136^{\circ}=44^{\circ}$.

Step3: Consider the given angle as the vertex - angle

If the given $68^{\circ}$ angle is the vertex - angle, let the base - angles be $y$ each. Then $68^{\circ}+2y = 180^{\circ}$ (by the angle - sum property of a triangle). Solving for $y$, we have $2y=180^{\circ}-68^{\circ}=112^{\circ}$, so $y = 56^{\circ}$.

Answer:

$56^{\circ}$, $44^{\circ}$, $68^{\circ}$