Step by step
The question
Question: find out if the two lines are parallel.
The alternate angles are 2x + 10 and 3x − 20, with x = 30.
1 Put x in
Put x = 30 in the angle 2x + 10.
2x + 10 = 2 × 30 + 10
That is 70°.
2x + 10 = 70
Put x = 30 in the angle 3x − 20.
3x − 20 = 3 × 30 − 20
That is 70°.
3x − 20 = 70
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 70°: they are equal.
70 = 70
Careful!
For alternate angles we ask: are they equal?
Careful: alternate: equal, not adding to 180°
So the lines are parallel.
Answer: = 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.
Answer
Answer: = parallel