give one pair of supplementary angles and one pair of vertical angles shown in the figure below. (a)…

Explanation:

Step1: Recall definitions

Supplementary angles add up to 180 degrees. Vertical - angles are opposite each other when two lines intersect.

Step2: Identify supplementary angles

For example, $\angle1$ and $\angle2$ form a linear - pair. Since a linear - pair of angles is supplementary, $\angle1+\angle2 = 180^{\circ}$.

Step3: Identify vertical angles

$\angle1$ and $\angle3$ are vertical angles as they are opposite each other when two lines intersect.

Answer:

(a) Supplementary angles: $\angle1$ and $\angle2$ (b) Vertical angles: $\angle1$ and $\angle3$