Question

give one pair of vertical angles and one pair of supplementary angles shown in the figure below. (a) vertical angles: \\( \angle \\) and \\( \angle \\) (b) supplementary angles: \\( \angle \\) and \\( \angle \\)

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are opposite angles formed by two intersecting lines. In the given figure, \(\angle1\) and \(\angle3\) are opposite angles formed by the intersection of line \(l\) and the transversal.

Step2: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). \(\angle1\) and \(\angle2\) form a linear - pair (they are adjacent and their non - common sides are opposite rays), so \(\angle1+\angle2 = 180^{\circ}\).

Answer:

(a) Vertical angles: \(\angle1\) and \(\angle3\)
(b) Supplementary angles: \(\angle1\) and \(\angle2\)