Question

find the measure of an exterior angle of a equilateral triangle (3 - sided polygon). exterior angle = ?°

Explanation:

Step1: Recall interior - angle of equilateral triangle

In an equilateral triangle, each interior angle is $60^{\circ}$ since the sum of interior angles of a triangle is $180^{\circ}$ and all angles are equal ($180\div3 = 60^{\circ}$).

Step2: Use the relationship between interior and exterior angles

The sum of an interior angle and its corresponding exterior angle of any polygon is $180^{\circ}$. Let the exterior angle be $x$. We have the equation $x + 60=180$.

Step3: Solve for the exterior angle

Subtract $60$ from both sides of the equation: $x=180 - 60$.
$x = 120^{\circ}$

Answer:

$120$