Question

an isosceles triangle has an angle that measures 80°. what measures are possible for the other two angles? choose all that apply. 80° 40° 50° 20°

Explanation:

Step1: Case 1 - Given angle is a base - angle

If the $80^{\circ}$ angle is a base - angle, then the other base - angle is also $80^{\circ}$ because in an isosceles triangle, the base - angles are equal. Let the third angle be $x$. Using the angle - sum property of a triangle ($x + 80^{\circ}+80^{\circ}=180^{\circ}$), we can solve for $x$.
$x=180^{\circ}-(80^{\circ}+80^{\circ}) = 20^{\circ}$

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

If the $80^{\circ}$ angle is the vertex - angle, let the base - angles be $y$ each. Using the angle - sum property of a triangle ($80^{\circ}+2y = 180^{\circ}$).
First, subtract $80^{\circ}$ from both sides: $2y=180^{\circ}-80^{\circ}=100^{\circ}$. Then divide both sides by 2: $y = 50^{\circ}$

Answer:

$80^{\circ}$, $20^{\circ}$, $50^{\circ}$