Question

one angle of an isosceles triangle measures 80°. what measures are possible for the other two angles? choose all that apply. 20° 50° 15° 80°

Explanation:

Step1: Consider 80° as the vertex - angle

In an isosceles triangle, the base - angles are equal. Let the base - angles be $x$. The sum of the interior angles of a triangle is 180°. So, $80 + 2x=180$. Solving for $x$:
$2x = 180 - 80$
$2x=100$
$x = 50^{\circ}$

Step2: Consider 80° as a base - angle

If one base - angle is 80°, then the other base - angle is also 80° (since base - angles of an isosceles triangle are equal). Let the vertex - angle be $y$. Then $y+80 + 80=180$.
$y=180-(80 + 80)$
$y = 20^{\circ}$

Answer:

A. $20^{\circ}$, B. $50^{\circ}$, D. $80^{\circ}$