Question

m∠x = \square°

Explanation:

Step1: Find sum of quadrilateral angles

The sum of interior angles of a quadrilateral is calculated by the formula $(n-2)\times180^\circ$, where $n=4$.
$$(4-2)\times180^\circ = 360^\circ$$

Step2: Find $\angle U$ in $RSTU$

Subtract known angles from total sum.
$$m\angle U = 360^\circ - 109^\circ - 72^\circ - 53^\circ = 126^\circ$$

Step3: Match angles for similar figures

Since $XYWZ \sim RSTU$, corresponding angles are equal: $\angle X \cong \angle T$, $\angle Y \cong \angle S$, $\angle Z \cong \angle R$, $\angle W \cong \angle U$. Thus $m\angle X = m\angle T$.
$$m\angle X = 72^\circ$$

Answer:

$72$