Answer
$x = 7$
Work Step by Step
According to theorem 6-16, the diagonals of a rhombus are perpendicular; therefore, the last angle in that triangle is a right angle.
According to the triangle sum theorem, the sum of the measures of the interior angles of a triangle equals $180^{\circ}$.
$(3x + 6) + (8x + 7) + 90 = 180$
Group like terms on the left side of the equation:
$(3x + 8x) + (6 + 7 + 90) = 180$
Combine like terms:
$11x + 103 = 180$
$11x = 77$
Divide each side by $11$ to solve for $x$:
$x = 7$
