Question

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

Explanation:

(a) A linear pair are adjacent angles forming a straight line (sum to $180^\circ$). $\angle1$ and $\angle2$ share a side and lie on line $l$.
(b) Vertical angles are opposite, equal angles formed by intersecting lines. $\angle1$ and $\angle3$ are opposite each other at the intersection of $l$ and $n$.
(c) Supplementary angles sum to $180^\circ$. $\angle2$ and $\angle4$ are a linear pair, so they are supplementary (any linear pair is supplementary, or non-adjacent angles like $\angle1$ and $\angle3$ do not sum to $180^\circ$, but $\angle2$ and $\angle4$ fit).

Answer:

(a) Linear pair: $\angle1$ and $\angle2$
(b) Vertical angles: $\angle1$ and $\angle3$
(c) Supplementary angles: $\angle2$ and $\angle4$

Note: Other valid pairs exist (e.g., (a) $\angle2$ & $\angle3$, (b) $\angle2$ & $\angle4$, (c) $\angle1$ & $\angle2$) but the above are correct examples.