Question

find one - pair of vertical angles and one pair of supplementary angles shown in the figure below. (a) vertical angles: ∠2 and ∠3 (b) supplementary angles: ∠1 and ∠2

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are opposite angles formed by two intersecting lines. In the given figure, when two lines intersect, ∠2 and ∠3 are opposite angles, so they are vertical angles.

Step2: Recall supplementary - angle definition

Supplementary angles are two angles whose sum is 180°. ∠1 and ∠2 form a linear - pair (adjacent angles on a straight line), and the sum of angles in a linear - pair is 180°, so ∠1 and ∠2 are supplementary angles.

Answer:

(a) Vertical angles: ∠2 and ∠3
(b) Supplementary angles: ∠1 and ∠2