Answer
$x = 12$
Work Step by Step
According to theorem 6-17, a rhombus has diagonals that bisect opposite angles. We can set the expressions equal to one another because these two angles are the result of being bisected by the diagonal of this rhombus:
$2x + 39 = 6x - 9$
Subtract $6x$ from each side of the equation to move variables to the left side of the equation:
$-4x + 39 = -9$
Subtract $39$ from each side of the equation to move constants to the right side of the equation:
$-4x = -48$
Divide both sides by $-4$ to solve for $x$:
$x = 12$
