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: Case 1 - Given angle is a base - angle

If the given $68^{\circ}$ angle is a base - angle, then the other base - angle is also $68^{\circ}$. Let the third angle be $x$. Using the angle - sum property of a triangle ($x + 68^{\circ}+68^{\circ}=180^{\circ}$), we can find $x$.
$x=180^{\circ}-(68^{\circ}+68^{\circ})=180^{\circ}-136^{\circ}=44^{\circ}$

Step2: Case 2 - Given angle is the vertex - angle

If the given $68^{\circ}$ angle is the vertex - angle, let the base - angles be $y$ each. Using the angle - sum property of a triangle ($68^{\circ}+2y = 180^{\circ}$). First, solve for $y$:
$2y=180^{\circ}-68^{\circ}=112^{\circ}$, then $y = 56^{\circ}$

Answer:

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