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

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are opposite angles formed by two intersecting lines. In the given figure, $\angle1$ and $\angle6$ are vertical angles. Also, $\angle2$ and $\angle5$, $\angle3$ and $\angle8$, $\angle4$ and $\angle7$ are vertical - angle pairs.

Step2: Recall linear - pair definition

A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays. $\angle1$ 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 $\angle5$ are linear - angle pairs.

Step3: Recall congruent - angle property

Vertical angles are always congruent. So, for congruent angles, we can choose $\angle1$ and $\angle6$ (or any other vertical - angle pair).

Answer:

(a) $\angle1$ and $\angle6$
(b) $\angle1$ and $\angle2$
(c) $\angle1$ and $\angle6$