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)
The angle that is a vertical pair with ∠1 is ∠3 since they have the same measure of 98°.
proof
To prove that ∠3 is a vertical pair with ∠1, we need to show that ∠3 and ∠1 are formed by the intersection of two lines and that they have the same measure.
Given that m∠1=98° and m∠3=98°, we can see that both angles have the same measure.
Now, to prove that ∠3 and ∠1 are formed by the intersection of two lines, we can describe the following diagram:
```
\ |
\ |
C |
\ |
\| ∠1
---------------A----------------
/|
/ |
/ |
/ |
/ |
∠3
```
In the diagram, line segment AC intersects line segment BA, forming angles ∠1 and ∠3 at point A.
Since ∠1 and ∠3 have the same measure (both equal to 98°) and they are formed by the intersection of two lines, we can conclude that ∠3 is a vertical pair with ∠1.
Therefore, we have proven that ∠3 is a vertical pair with ∠1.