Question

geometry, measurement, data analysis 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 opposite angles formed by the intersection of two lines. In the given figure, when two lines intersect, $\angle1$ and $\angle3$ are opposite to each other.

Step2: Recall supplementary - angle definition

Supplementary angles are two angles whose sum is $180^{\circ}$. Adjacent angles on a straight - line are supplementary. For example, $\angle1$ and $\angle2$ lie on the straight - line $l$ and $\angle1+\angle2 = 180^{\circ}$.

Answer:

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