Question

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

Explanation:

Step1: 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. A linear pair of angles is supplementary. So, \(\angle1+\angle2 = 180^{\circ}\) (another possible pair could be \(\angle1\) and \(\angle4\) etc., based on the linear - pair property).

Step2: Recall the definition of vertical angles

Vertical angles are the angles opposite each other when two lines cross. In the given figure, when two lines intersect, \(\angle1\) and \(\angle3\) are opposite each other. So, \(\angle1\) and \(\angle3\) are vertical angles (another possible pair could be \(\angle2\) and \(\angle4\) etc.).

Answer:

(a) Supplementary angles: \(\angle1\) and \(\angle2\) (or other valid linear - pair combinations like \(\angle1\) and \(\angle4\), \(\angle2\) and \(\angle3\), \(\angle3\) and \(\angle4\))
(b) Vertical angles: \(\angle1\) and \(\angle3\) (or other valid vertical - angle combinations like \(\angle2\) and \(\angle4\), \(\angle5\) and \(\angle7\), \(\angle6\) and \(\angle8\))