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: \\( \angle \square \\) and \\( \angle \square \\)
(b) vertical angles: \\( \angle \square \\) and \\( \angle \square \\)
(c) supplementary angles: \\( \angle \square \\) and \\( \angle \square \\)

Explanation:

Step1: Recall definitions

• Linear pair: Two adjacent angles that form a straight line. Their sum is \(180^{\circ}\). For example, \(\angle1\) and \(\angle2\) are adjacent and form a straight line.
• Vertical angles: Two non - adjacent angles formed by two intersecting lines. They are equal. For example, \(\angle1\) and \(\angle3\) are formed by the intersection of two lines \(l\) and \(n\).
• Supplementary angles: Two angles whose sum is \(180^{\circ}\). A linear pair is a special case of supplementary angles. But non - adjacent angles can also be supplementary. For example, \(\angle1\) and \(\angle5\) (if we assume some parallel line properties or just based on the sum concept. Another example, using the linear pair idea, \(\angle6\) and \(\angle7\) form a linear pair (sum \(180^{\circ}\))

Answer:

(a) Linear pair: \(\angle1\) and \(\angle2\) (or \(\angle3\) and \(\angle4\), \(\angle6\) and \(\angle7\), \(\angle5\) and \(\angle8\))
(b) Vertical angles: \(\angle1\) and \(\angle3\) (or \(\angle2\) and \(\angle4\), \(\angle6\) and \(\angle8\), \(\angle5\) and \(\angle7\))
(c) Supplementary angles: \(\angle1\) and \(\angle2\) (or any linear pair from part (a) or other pairs like \(\angle2\) and \(\angle5\) if we consider the sum of angles around a point or using parallel line angle - sum properties. For simplicity, using the linear pair as supplementary (since linear pair implies supplementary))