## Geometry: Common Core (15th Edition)

Each of the exterior angles has a measure of $120^{\circ}$.
We have an equiangular triangle, which means that each of the three interior angles has the same measure. If all the interior angles of a triangle add up to $180^{\circ}$, then $3$ (interior angles) of the equiangular triangle should equal $180^{\circ}$. Let's set up that equation to find the measure of one of the interior angles: $3$(interior angles) = $180$ Divide each side of the equation by $3$ to find the measure of one of the interior angles: interior angle = $60$ Now we know that each angle in this equiangular triangle is $60^{\circ}$. To find the measure of the exterior angle, we can use the exterior angle theorem, which states that the exterior angle of a triangle is equal to the sum of the two other interior angles, each of which is $60^{\circ}$. Let's set up that equation: exterior angle = $60 + 60$ exterior angle = $120$ Each of the exterior angles has a measure of $120^{\circ}$.