Question

m∠opq = m∠por because they are alternate interior angles.
m∠pqo = m∠qos because they are alternate interior angles.
m∠por + x° + m∠qos = 180° because the three angles form a straight line.
so the value of x must be

Explanation:

Step1: Identify equal alternate angles

From given, $m\angle POR = m\angle OPQ = 59^\circ$, $m\angle QOS = m\angle PQO = 53^\circ$

Step2: Use straight angle sum rule

The angles $\angle POR$, $x^\circ$, $\angle QOS$ sum to $180^\circ$. Substitute values:
$59^\circ + x^\circ + 53^\circ = 180^\circ$

Step3: Solve for $x$

Calculate sum of known angles: $59+53=112$. Rearrange:
$x = 180 - 112$

Answer:

$68^\circ$