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: ∠1 and ∠2 (b) vertical angles: ∠5 and ∠7 (c) supplementary angles: ∠6 and ∠7

Explanation:

• (a) Linear Pair: A linear pair of angles is formed when two adjacent angles are supplementary (sum to \(180^{\circ}\)). In the figure, \(\angle1\) and \(\angle2\) are adjacent and form a straight - line (their non - common sides are opposite rays), so they form a linear pair.
• (b) Vertical Angles: Vertical angles are the non - adjacent angles formed by the intersection of two lines. When lines \(m\) and \(n\) intersect, \(\angle5\) and \(\angle7\) are opposite each other, so they are vertical angles.
• (c) Supplementary Angles: Two angles are supplementary if their sum is \(180^{\circ}\). \(\angle6\) and \(\angle7\) are adjacent and form a linear pair (their non - common sides are opposite rays), so \(\angle6+\angle7 = 180^{\circ}\), making them supplementary.

Answer:

(a) \(\angle1\) and \(\angle2\)
(b) \(\angle5\) and \(\angle7\)
(c) \(\angle6\) and \(\angle7\)