Step by step
The question
Question: find out if the two lines are parallel.
The alternate angles are 4x − 10 and 3x + 15, with x = 20.
1 Put x in
Put x = 20 in the angle 4x − 10.
4x − 10 = 4 × 20 − 10
That is 70°.
4x − 10 = 70
Put x = 20 in the angle 3x + 15.
3x + 15 = 3 × 20 + 15
That is 75°.
3x + 15 = 75
2 Name the angle pair
A line crosses two other lines.
It is called a transversal.
Our two angles are between the lines, on opposite sides of the transversal: alternate angles.
Together they make a Z shape.
3 Use the parallel test
Parallel lines make alternate angles equal.
And if they are equal, the lines are parallel.
70° and 75° are not equal.
70 ≠ 75
Careful!
For alternate angles we ask: are they equal?
Careful: alternate: equal, not adding to 180°
So the lines are not parallel.
Answer: = not parallel
If we carry the lines on, they would meet.
Look at the picture: the top line is turned.
Let's look back.
First: put x in.
Then: name the angle pair.
Last: use the parallel test.
Answer
Answer: = not parallel