Answer
$x = 24$
Work Step by Step
If two lines are cut by a transversal and alternate interior angles are congruent, then those lines are parallel.
Let's set the two angles equal to one another:
$m \angle BAC = m \angle DCA$
Plug in our knowns from the diagram: $2x + 15 = 4x - 33$
Subtract $15$ from each side of the equation to move constants to the right side of the equation:
$2x = 4x - 48$
Subtract $4x$ from each side of the equation to move the variable to the left side of the equation:
$-2x = -48$
Divide both sides of the equation by $-2$ to solve for $x$:
$x = 24$
