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

• A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays.
• Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines.
• Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Identify linear pair

For part (a), \(\angle2\) and \(\angle4\) are adjacent angles and their non - common sides are opposite rays (since lines \(l\) and \(n\) intersect).

Step3: Identify vertical angles

For part (b), \(\angle6\) and \(\angle8\) are non - adjacent angles formed by the intersection of lines \(m\) and \(n\).

Step4: Identify supplementary angles

For part (c), \(\angle3\) and \(\angle5\) (assuming they are on a straight line conceptually, as when two lines are intersected by a transversal etc., we can consider angles that sum to \(180^{\circ}\)).

Answer:

(a) Linear pair: \(\angle2\) and \(\angle4\)
(b) Vertical angles: \(\angle6\) and \(\angle8\)
(c) Supplementary angles: \(\angle3\) and \(\angle5\)