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) Linear pair: A linear pair of angles is formed when two adjacent angles form a straight line. In the figure, \(\angle1\) and \(\angle2\) are adjacent and their non - common sides form a straight line (line \(l\)).
• (b) Vertical angles: Vertical angles are the opposite angles formed by the intersection of two lines. When two lines intersect (here, line \(l\) and line \(n\)), \(\angle1\) and \(\angle4\) are opposite each other.
• (c) Supplementary angles: Supplementary angles are two angles whose sum is \(180^{\circ}\). A linear pair of angles is always supplementary. Since \(\angle1\) and \(\angle2\) form a linear pair, they are supplementary.

Answer:

(a) \(\angle1\) and \(\angle2\)
(b) \(\angle1\) and \(\angle4\)
(c) \(\angle1\) and \(\angle2\)