Question

for the figure below, give the following.
(a) one pair of vertical angles
(b) one pair of angles that form a linear pair
(c) one pair of angles that are supplementary

Explanation:

• (a) Vertical angles are opposite angles formed by two intersecting lines. In the figure, \(\angle1\) and \(\angle3\) (or \(\angle2\) and \(\angle4\), \(\angle5\) and \(\angle7\), \(\angle6\) and \(\angle8\)) are vertical angles.
• (b) A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays. \(\angle1\) and \(\angle2\) (or \(\angle2\) and \(\angle3\), \(\angle3\) and \(\angle4\), \(\angle4\) and \(\angle1\), \(\angle5\) and \(\angle6\), \(\angle6\) and \(\angle7\), \(\angle7\) and \(\angle8\), \(\angle8\) and \(\angle5\)) form a linear pair.
• (c) Supplementary angles are two angles whose sum is \(180^{\circ}\). A linear pair of angles is always supplementary. So, for example, \(\angle1\) and \(\angle2\) (or any of the linear pairs mentioned above) are supplementary.

Answer:

(a) \(\angle1\) and \(\angle3\) (or other valid vertical angle pairs)
(b) \(\angle1\) and \(\angle2\) (or other valid linear - pair angle pairs)
(c) \(\angle1\) and \(\angle2\) (or other valid supplementary angle pairs)