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
(a) vertical angles: ∠ and ∠
(b) linear pair: ∠ and ∠
(c) supplementary angles: ∠ and ∠

Explanation:

• Vertical angles: Vertical angles are opposite angles formed by the intersection of two lines. In the given figure, \(\angle1\) and \(\angle3\) (or \(\angle2\) and \(\angle4\), \(\angle6\) and \(\angle8\), \(\angle5\) and \(\angle7\)) are vertical angles.
• Linear pair: A linear pair of angles is adjacent angles that form a straight line (sum to \(180^{\circ}\)). For example, \(\angle1\) 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.
• Supplementary angles: Supplementary angles are two angles whose sum is \(180^{\circ}\). Vertical angles (e.g., \(\angle1\) and \(\angle3\)) are not a linear pair but are supplementary (since vertical angles are equal and if two vertical angles are each \(90^{\circ}\) they are supplementary, and in general, if two lines intersect, the sum of a pair of vertical angles can be considered in the context of the straight - line angles around the intersection). Also, angles in a linear pair are supplementary. Another non - linear pair supplementary example could be if we consider parallel lines and transversals (but in the basic intersection of lines case, linear pair angles are a sure - fire example of supplementary angles).

Answer:

(a) \(\angle1\) and \(\angle3\) (or other valid vertical - angle pairs)
(b) \(\angle1\) and \(\angle2\) (or other valid linear - pair pairs)
(c) \(\angle1\) and \(\angle2\) (linear - pair angles are supplementary, or other pairs like \(\angle5\) and \(\angle7\) if we assume some angle - measure relationships from the intersection of lines)