Question

$mangle rst = mangle sru$ because they are alternate interior angles.$mangle str = mangle trv$ because they are alternate interior angles.$mangle sru + x^circ + mangle trv =$ $qquad$ $\backsim$ because the three angles$\backsim$

Explanation:

Step1: Identify alternate interior angles

From given: $m\angle RST = m\angle SRU = 50^\circ$, $m\angle STR = m\angle TRV = 72^\circ$

Step2: Use straight angle sum rule

Angles on a straight line sum to $180^\circ$.
$m\angle SRU + x^\circ + m\angle TRV = 50^\circ + x^\circ + 72^\circ = 180^\circ$

Step3: Solve for $x$

$x^\circ = 180^\circ - 50^\circ - 72^\circ$
$x^\circ = 58^\circ$

Answer:

$m\angle SRU + x^\circ + m\angle TRV = 180^\circ$ because the three angles form a straight angle.
The value of $x$ is $\boldsymbol{58}$