Answer
The angle measures $77^{\circ}$..
Work Step by Step
Let $y$ be the measure of an angle and $x$ be the measure of its complement.
$y = 5x + 12$
We have the equation:
$x + y = 90$
Substitute $5x + 12$ for $y$:
$x + (5x + 12) = 90$
Combine like terms:
$6x + 12 = 90$
Subtract $12$ from both sides of the equation to move constants to the right side of the equation:
$6x = 78$
Divide both sides by $6$ to solve for $x$:
$x = 13$
We can substitute $13$ for $x$ in the equation to find $y$, the length of the angle we are looking for:
$y = 5(13) + 12$
Multiply first:
$y = 65 + 12$
Add to solve:
$y = 77$
The angle measures $77^{\circ}$.
