Question

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

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are opposite angles formed by the intersection of two lines. In the given figure, \(\angle2\) and \(\angle4\) are opposite angles formed by the intersection of line \(l\) and the horizontal line.

Step2: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). In the given figure, \(\angle1\) and \(\angle2\) form a linear - pair (they are adjacent and their non - common sides form a straight line). So, \(\angle1+\angle2 = 180^{\circ}\)

Answer:

(a) Vertical angles: \(\angle2\) and \(\angle4\)
(b) Supplementary angles: \(\angle1\) and \(\angle2\) (Note: There are other valid pairs for both vertical and supplementary angles. For vertical angles, \(\angle1\) and \(\angle3\), \(\angle6\) and \(\angle8\), \(\angle5\) and \(\angle7\) are also vertical angle pairs. For supplementary angles, \(\angle3\) and \(\angle4\), \(\angle5\) and \(\angle6\), \(\angle7\) and \(\angle8\) etc. are also supplementary angle pairs)