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:

Step1: Recall definitions

• Linear pair: Two adjacent angles that form a straight line ($180^{\circ}$).
• Vertical angles: Opposite angles formed by two intersecting lines.
• Supplementary angles: Two angles whose sum is $180^{\circ}$.

Step2: Identify linear pair

Looking at the figure, $\angle1$ and $\angle2$ are adjacent and form a straight line.

Step3: Identify vertical angles

$\angle5$ and $\angle7$ are opposite angles formed by the intersection of lines $m$ and $n$.

Step4: Identify supplementary angles

$\angle6$ and $\angle7$ are adjacent and form a straight line (also, sum to $180^{\circ}$).

Answer:

(a) Linear pair: $\angle1$ and $\angle2$
(b) Vertical angles: $\angle5$ and $\angle7$
(c) Supplementary angles: $\angle6$ and $\angle7$