Question

geometry. measurement. data. identifying supplementary and vertical angles. 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 - angle definition

Vertical angles are formed when two lines intersect and are opposite each other. In the given figure, when two lines intersect, $\angle1$ and $\angle2$ are vertical angles (also $\angle3$ and $\angle4$, $\angle5$ and $\angle6$, $\angle7$ and $\angle8$). Let's choose $\angle1$ and $\angle2$.

Step2: Recall supplementary - angle definition

Supplementary angles are two angles whose sum is $180^{\circ}$. Adjacent angles formed by two intersecting lines are supplementary. For example, $\angle1$ and $\angle5$ are supplementary.

Answer:

(a) Vertical angles: $\angle1$ and $\angle2$
(b) Supplementary angles: $\angle1$ and $\angle5$