Question

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

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles sum to \(180^\circ\). Adjacent angles on a straight line are supplementary. For example, \(\angle1\) and \(\angle2\) form a linear pair, so \(\angle1 + \angle2 = 180^\circ\), making them supplementary.

Step2: Recall Vertical Angles

Vertical angles are opposite angles formed by intersecting lines, and they are equal. For example, \(\angle1\) and \(\angle3\) are vertical angles (formed by the intersection of two lines), so \(\angle1=\angle3\).

Answer:

(a) Supplementary angles: \(\angle1\) and \(\angle2\) (or other valid pairs like \(\angle2\) and \(\angle3\), \(\angle3\) and \(\angle4\), \(\angle4\) and \(\angle1\), \(\angle5\) and \(\angle6\), etc.)
(b) Vertical angles: \(\angle1\) and \(\angle3\) (or other valid pairs like \(\angle2\) and \(\angle4\), \(\angle5\) and \(\angle7\), \(\angle6\) and \(\angle8\))