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: \\( \angle \square \\) and \\( \angle \square \\) (b) linear pair: \\( \angle \square \\) and \\( \angle \square \\) (c) supplementary angles: \\( \angle \square \\) and \\( \angle \square \\)

Explanation:

Step1: Identify vertical angles

Vertical angles are opposite angles formed by two intersecting lines. In the figure, $\angle1$ and $\angle3$ are vertical angles (another possible pair is $\angle2$ and $\angle4$, $\angle5$ and $\angle7$, $\angle6$ and $\angle8$).

Step2: Identify linear - pair angles

A linear pair of angles is adjacent angles that form a straight line (sum to $180^{\circ}$). $\angle1$ and $\angle2$ form a linear pair (other possible pairs: $\angle2$ and $\angle3$, $\angle3$ and $\angle4$, $\angle4$ and $\angle8$, $\angle8$ and $\angle7$, $\angle7$ and $\angle3$, $\angle6$ and $\angle5$, $\angle6$ and $\angle2$ etc.).

Step3: Identify supplementary angles

Supplementary angles are two angles whose sum is $180^{\circ}$. A linear pair is a special case of supplementary angles. Also, non - adjacent angles can be supplementary. For example, $\angle1$ and $\angle3$ are vertical angles. If we consider $\angle1$ and $\angle7$, since $\angle1+\angle2 = 180^{\circ}$ and $\angle2=\angle7$ (vertical angles), then $\angle1+\angle7=180^{\circ}$. Another simple case is using the linear pair. Let's use the linear pair for simplicity.

Answer:

(a) Vertical angles: $\angle1$ and $\angle3$ (or other valid vertical - angle pairs)
(b) Linear pair: $\angle1$ and $\angle2$ (or other valid linear - pair pairs)
(c) Supplementary angles: $\angle1$ and $\angle2$ (or other valid supplementary - angle pairs)