Question

for the figure below, give the following. (a) one pair of vertical angles (b) one pair of angles that form a linear pair (c) one pair of angles that are supplementary

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are opposite angles formed by the intersection of two lines. In the given figure, $\angle2$ and $\angle4$ are vertical angles (also $\angle1$ and $\angle3$, $\angle6$ and $\angle8$, $\angle5$ and $\angle7$). We can choose $\angle2$ and $\angle4$.

Step2: Recall linear - pair definition

A linear pair of angles are adjacent angles that form a straight - line. $\angle1$ and $\angle2$ form a linear pair (also $\angle2$ and $\angle3$, $\angle3$ and $\angle4$, $\angle4$ and $\angle1$, $\angle5$ and $\angle6$, $\angle6$ and $\angle7$, $\angle7$ and $\angle8$, $\angle8$ and $\angle5$). We can choose $\angle1$ and $\angle2$.

Step3: Recall supplementary - angle definition

Supplementary angles are two angles whose sum is $180^{\circ}$. A linear pair of angles is always supplementary. Since $\angle1$ and $\angle2$ form a linear pair, they are supplementary.

Answer:

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