Parallel Lines Proof: Analyzing Angles 2X+10 and 70-X

Question

Are lines AB and DC parallel?

00:00 Are the lines parallel?

00:02 To find out, let's assume they are parallel and try to find X

00:05 Corresponding angles are equal between parallel lines

00:09 Therefore, we'll equate the angles and solve for X

00:15 Let's isolate X

00:20 Since there is a solution for X, the lines are parallel

00:27 Let's substitute the solution we found for X and find the angles

00:39 And this is the solution to the question

For the lines to be parallel, the two angles must be equal (according to the definition of corresponding angles).

Let's compare the angles:

$2x+10=70-x$

$2x+x=70-10$

$3x=60$

$x=20$

Once we have worked out the variable, we substitute it into both expressions to work out how much each angle is worth.

First, substitute it into the first angle:

$2x+10=2\times20+10$

$40+10=50$

Then into the other one:

$70-20=50$

We find that the angles are equal and, therefore, the lines are parallel.

Yes