Question

give one pair of vertical angles and one pair of supplementary angles shown in the figure below.

Explanation:

Step1: Recall vertical - angle definition

Vertical angles are opposite angles formed by the intersection of two lines. In the given figure, when two lines intersect, ∠1 and ∠6 are vertical angles (also ∠2 and ∠5, ∠3 and ∠8, ∠4 and ∠7 are vertical - angle pairs). We can choose ∠1 and ∠6.

Step2: Recall supplementary - angle definition

Supplementary angles are two angles whose sum is 180°. Adjacent angles formed by two intersecting lines are supplementary. For example, ∠1 and ∠2 are supplementary (also many other adjacent - angle pairs like ∠2 and ∠3, ∠3 and ∠4, ∠4 and ∠1, ∠5 and ∠6, ∠6 and ∠7, ∠7 and ∠8, ∠8 and ∠5). We can choose ∠1 and ∠2.

Answer:

(a) Vertical angles: ∠1 and ∠6
(b) Supplementary angles: ∠1 and ∠2