## Geometry: Common Core (15th Edition)

$m \angle 3 = 120$
Complementary angles are angles that add up to $90^{\circ}$. Supplementary angles are those that add up to $180^{\circ}$. If $\angle 1$ and $\angle 2$ are complementary, then they add up to $90^{\circ}$. If $m \angle 2$ is $30^{\circ}$, then we find $m \angle 1$ by the following equation: $m \angle 1 = 90 - m \angle 2$ Let's plug in what we know: $m \angle 1 = 90 - 30$ Subtract to solve: $m \angle 1 = 60$ If we know that $\angle 1$ is supplementary to $\angle 3$, then we can use the following equation to determine $m \angle 3$: $m \angle 3 = 180 - m \angle 1$ Let's plug in our value for $m \angle 1$: $m \angle 3 = 180 - 60$ Subtract to solve: $m \angle 3 = 120$