In the given diagram, you have two parallel lines $PR$ and $SU$ with a transversal line intersecting them. You are provided with the information that:

• $PR \parallel SU$
• $\angle PQT = 136^\circ$

You are asked to find the measure of $\angle RQO$.

Since $PR$ and $SU$ are parallel lines, and $PQT$ and $RQO$ are angles on the same side of the transversal, we can apply the concept of supplementary angles. Supplementary angles sum up to $180^\circ$.

The angles $\angle PQT$ and $\angle RQO$ form a linear pair, so:

$\angle PQT + \angle RQO = 180^\circ$

Given that $\angle PQT = 136^\circ$, we can solve for $\angle RQO$:

$\angle RQO = 180^\circ - 136^\circ = 44^\circ$

Thus, the measure of $\angle RQO$ is $44^\circ$.

Would you like further explanation or details?

Related Questions:

1. What are alternate interior angles, and how do they apply to parallel lines?
2. How do we prove that two angles are supplementary?
3. Can we identify any corresponding angles in this diagram?
4. What is the definition of a transversal, and how does it affect parallel lines?
5. What other angle relationships can be found in this diagram?

Tip: Always remember that angles on a straight line (linear pair) add up to $180^\circ$.