Question

give one pair of vertical angles and one pair of supplementary angles shown in the figure below.

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are opposite angles formed by two intersecting lines. In the given figure, when two lines intersect, $\angle2$ and $\angle4$ (or $\angle1$ and $\angle3$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$) are vertical - angle pairs. Let's choose $\angle2$ and $\angle4$.

Step2: Recall supplementary - angle definition

Supplementary angles are two angles whose sum is $180^{\circ}$. Adjacent angles formed by two intersecting lines are supplementary. For example, $\angle1$ and $\angle2$ (or $\angle2$ and $\angle3$, $\angle3$ and $\angle4$, $\angle4$ and $\angle1$, $\angle5$ and $\angle6$, $\angle6$ and $\angle7$, $\angle7$ and $\angle8$, $\angle8$ and $\angle5$) are supplementary - angle pairs. Let's choose $\angle1$ and $\angle2$.

Answer:

(a) $\angle2$ and $\angle4$
(b) $\angle1$ and $\angle2$