Question

give one pair of vertical angles and one pair of supplementary angles shown in the figure below. (a) vertical angles: ∠ and ∠ (b) supplementary angles: ∠1 and ∠5

Explanation:

Step1: Recall vertical - angles definition

Vertical angles are opposite angles formed by two intersecting lines.

Step2: Identify vertical - angle pair

In the given figure, $\angle1$ and $\angle2$ are vertical angles (or $\angle3$ and $\angle4$, $\angle5$ and $\angle6$, $\angle7$ and $\angle8$). We can choose $\angle1$ and $\angle2$.

Step3: Recall supplementary - angles definition

Supplementary angles are two angles whose sum is $180^{\circ}$. Adjacent angles on a straight - line are supplementary.

Step4: Identify supplementary - angle pair

$\angle1$ and $\angle5$ are supplementary as they are adjacent angles on a straight - line.

Answer:

(a) Vertical angles: $\angle1$ and $\angle2$
(b) Supplementary angles: $\angle1$ and $\angle5$