Question

Question

Four angles share a vertex. m∠1=98°, m∠2=82°, m∠3=98°, and m∠4=82°. Which angle is a vertical pair with ∠1?(1 point)
Responses

∠3
angle 3

none
none

∠2
angle 2

∠4

Answer 1

When four angles share a vertex, they can form two pairs of vertical angles. Vertical angles are opposite each other when two lines intersect, and they have the same measure.

Given the angles and their measures:
- $\mathrm{\angle }1={98}^{\circ }$
- $\mathrm{\angle }2={82}^{\circ }$
- $\mathrm{\angle }3={98}^{\circ }$
- $\mathrm{\angle }4={82}^{\circ }$

Since $\mathrm{\angle }1$ and $\mathrm{\angle }3$ both have measures of ${98}^{\circ }$, they are a pair of vertical angles.

So, $\mathrm{\angle }3$ is the angle that is a vertical pair with $\mathrm{\angle }1$.

Therefore, the answer is:
$\mathrm{\angle }3$.