Why can you use Linear Pairs and Vertical Angles to prove lines are parallel?

The reason why linear pairs and vertical angles are used to prove lines are parallel is because they area transversal drawn through the parallel lines will form angles on each of the two parallel lines including;

1) Supplementary linear pairs  and

2) Vertical angles

3) Alternate angles

Given that either;

a) The corresponding angles that form the linear pairs are congruent

b) The corresponding vertically opposite angles are congruent

c) The corresponding alternate angles are congruent, we have;

The two lines are said to be parallel.

Step-by-step explanation:

518,400

step-by-step explanation:

the area is multiplying all the given measurements together.

40 * 18 * 30 * 24 = 518,400

m∠a is 90°

m∠b is 40°