Iam having a hard time with this proof of vertical angles. the choices for them are at the bottom.

Angles 1 and 3 are verical: Given

Angles 1 and 3 are formed by ntersecting lines:

Definition of vertical angles.

Angles 1 and 2 are a linear pair and angles 2 and 3 are a linear pair:

Definition of linear pair.

1 and 2 are supplementary, and 2 and 3 are supplementary:

Linear Pair Theorem

Angles 1 and 3 are congruent:

Congruent Supplement Theorem

Step-by-step explanation:

The first is given because it tells you it is given.

The second is the definition of vertical angles. Vertical angles are angles formed by two intersecting lines.

The third statement is the definition of linear pair. Linear pair is a pair of adjacent angles formed by two lines that intersect.

The fourth statement comes from the theorem of linear pairs.  Linear pair theorem states that if you have 2 angles that are a linear pair, then they are supplementary.

The fifth statement comes from the congruent supplement theorem. It says if 2 angles are supplementary to the same angle, then they are congruent to each other.