Answer
Angle 1 has a measure of $42^{\circ}$.
Work Step by Step
We are given that one of the interior angles of the triangle measures $78^{\circ}$. We also have the measure of an exterior angle, which is $120^{\circ}$. According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two other interior angles. Let's set up that equation:
$120 = \angle 1 + 78$
Subtract $78$ from each side of the equation to solve for the measure of $\angle 1$:
$\angle 1 = 42$
Angle 1 has a measure of $42^{\circ}$.
