## Geometry: Common Core (15th Edition)

$m \angle 1 = 52^{\circ}$
Using the triangle-sum theorem, which states that the sum of the interior angles of a triangle equal $180^{\circ}$, we can find $m \angle 1$. We have an angle in the triangle that is complementary to the angle that measures $31^{\circ}$. Therefore, that complementary angle is $90 - 31$ or $59^{\circ}$. Now, that we have the measures of two angles in that triangle, we can use the triangle-sum theorem to write an equation: $m \angle 1 = 180 - (69 + 59)$ Evaluate what is in parentheses first: $m \angle 1 = 180 - (128)$ Subtract to solve: $m \angle 1 = 52^{\circ}$