#### Answer

Each of the exterior angles has a measure of $120^{\circ}$.

#### Work Step by Step

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 $120^{\circ}$.