Question

select all the pairs of supplementary angles.
∠rqo and ∠utq
∠pqo and ∠rqo
∠pqo and ∠pqt
∠rqt and ∠pqt

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180 degrees.

Step2: Analyze linear - pair angles

• $\angle PQO$ and $\angle RQO$ form a linear pair. A linear - pair of angles are supplementary. So, $\angle PQO+\angle RQO = 180^{\circ}$.
• $\angle PQO$ and $\angle PQT$ form a linear pair. So, $\angle PQO+\angle PQT = 180^{\circ}$.
• $\angle RQT$ and $\angle PQT$ form a linear pair. So, $\angle RQT+\angle PQT = 180^{\circ}$.
• $\angle RQO$ and $\angle UTQ$: Since $PR\parallel SU$ and $OV$ is a transversal, $\angle RQO$ and $\angle UTQ$ are corresponding angles. Also, considering the linear - pair relationships and angle - sum properties, we can show that they are supplementary.

Answer:

$\angle RQO$ and $\angle UTQ$, $\angle PQO$ and $\angle RQO$, $\angle PQO$ and $\angle PQT$, $\angle RQT$ and $\angle PQT$