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 Vertical Angles

Vertical angles are opposite angles formed by two intersecting lines. So, for example, ∠1 and ∠3 are vertical angles (or ∠2 and ∠4, ∠5 and ∠7, ∠6 and ∠8). Let's pick ∠1 and ∠3.

Step2: Recall Supplementary Angles

Supplementary angles are two angles whose sum is 180°. Angles on a straight line are supplementary. For example, ∠1 and ∠2 are supplementary (or ∠3 and ∠4, ∠5 and ∠6, ∠7 and ∠8, etc.). Let's pick ∠1 and ∠2.

Answer:

(a) Vertical angles: $\angle 1$ and $\angle 3$ (or other valid pair like $\angle 2$ and $\angle 4$, $\angle 5$ and $\angle 7$, $\angle 6$ and $\angle 8$)
(b) Supplementary angles: $\angle 1$ and $\angle 2$ (or other valid pair like $\angle 3$ and $\angle 4$, $\angle 5$ and $\angle 6$, $\angle 7$ and $\angle 8$, etc.)

(Note: There are multiple correct answers. For example, another vertical pair could be $\angle 5$ and $\angle 7$, and another supplementary pair could be $\angle 5$ and $\angle 6$.)