Answer
$x = 30$
Work Step by Step
We have a figure that is a parallelogram. Opposite angles of a parallelogram are congruent.
We are given the measure of an exterior angle that is supplementary to this opposite angle.
measure of interior angle = $180^{\circ} - 45^{\circ}$
Subtract to solve:
measure of interior angle = $135^{\circ}$
We now know that the opposite angle is also $135^{\circ}$. Let's set the expression equal to this value to solve for $x$:
$(4x + 15)^{\circ} = 135^{\circ}$
Subtract $15$ from each side of the equation to move constants to the right side of the equation:
$4x = 120$
Divide both sides by $4$ to solve for $x$:
$x = 30$
