Answer
Both the angle of elevation and the angle of depression are $46^{\circ}$.
Work Step by Step
For this exercise, the angle of elevation and the angle of depression are the same because they are actually alternate interior angles, and alternate interior angles are congruent to one another.
Let's set the angle of elevation $e$ equal to the angle of depression $d$:
$3x + 1 = 2(x + 8)$
Distribute on the right side of the equation:
$3x + 1 = 2x + 16$
Subtract $2x$ from each side of the equation to move variables to the left side of the equation:
$x + 1 = 16$
Subtract $1$ from each side of the equation to solve for $x$:
$x = 15$
We are asked to find $e$ and $d$, which are congruent to one another.
Let's set up the expression to find $e$:
$e = 3x + 1$
Plug in $15$ for $x$:
$e = 3(15) + 1$
Multiply first, according to order of operations:
$e = 45 + 1$
Add to solve for $e$:
$e = 46^{\circ}$
Both $e$ and $d$ are congruent; therefore:
$d = 46^{\circ}$
