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 (a) vertical angles: ∠ and ∠ (b) linear pair: ∠ and ∠ (c) supplementary angles: ∠ and ∠

Explanation:

Step1: Recall vertical - angle definition

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

Step2: Recall linear - pair definition

A linear pair of angles are adjacent angles that form a straight - line. $\angle1$ 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 linear pairs. Let's choose $\angle1$ and $\angle2$.

Step3: Recall supplementary - angle definition

Supplementary angles are two angles whose sum is $180^{\circ}$. Linear pairs are supplementary. So, we can choose the same pair as in the linear - pair case. Let's choose $\angle1$ and $\angle2$.

Answer:

(a) $\angle1$ and $\angle3$
(b) $\angle1$ and $\angle2$
(c) $\angle1$ and $\angle2$