Answer
$m \angle x = 68^{\circ}$
Work Step by Step
The diagonals of a kite cross each other at right angles. Now, we have the measures of two of the angles of the triangle that contains $\angle x$, so let's set up the equation to find the measure of this angle using the triangle-sum theorem, which states that the sum of the measures of the interior angles of a triangle is $180^{\circ}$.
$m \angle x = 180 - (90 + 22)$
Evaluate what is in parentheses first:
$m \angle x = 180 - (112)$
Subtract to solve:
$m \angle x = 68^{\circ}$
