Step by step
The question
Question: find out if the two lines are parallel.
The co-interior angles are x + 40 and 2x + 20, with x = 40.
1 Put x in
Put x = 40 in the angle x + 40.
That is 80°.
Put x = 40 in the angle 2x + 20.
That is 100°.
2 Name the angle pair
A line crosses two other lines.
It is called a transversal.
Our two angles are between the lines, on the same side of the transversal: co-interior angles.
Together they make a C shape.
3 Use the parallel test
Parallel lines make co-interior angles add up to 180°.
And if they add up to 180°, the lines are parallel.
So we add them: 80 + 100 = 180.
180 is 180.
They add up to 180°.
Careful!
For co-interior angles we do not ask: are they equal?
We ask: do they add up to 180°?
So the lines are parallel.
We can draw the arrows on the lines now.
Let's look back.
First: put x in.
Then: name the angle pair.
Last: use the parallel test.