Step by step
The question
Question: find x.
The two lines are parallel.
The corresponding angles are 2x and 3x + 20.
1 Use the angle fact
The arrows show the two lines are parallel.
Parallel lines go the same way.
They never meet.
A third line crosses both of them.
It is called a transversal.
Our two angles are in the same place at each crossing.
They are called corresponding angles.
Together they make an F shape.
The lines go the same way, so both crossings look the same.
So corresponding angles are equal.
So the two angles are equal: 2x = 3x + 20.
2 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 2x from the left side.
To remove 2x, we take away 2x.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
2x and − 2x make zero.
Cross them out.
3x − 2x = x.
Now we have 0 = x + 20.
Let's swap the two sides, so x is on the left.
3 Remove the + 20
We want x by itself.
The + 20 is in the way.
To remove + 20, we take away 20.
We do it on both sides, so they stay equal.
+ 20 and − 20 make zero.
Cross them out.
0 − 20 = −20.
So x = −20!
4 Check
Let's check: put x = −20 in the angle 2x.
We get −40°.
An angle between two lines is always more than 0°.
So this is impossible.
Let's look back.
First: use the angle fact.
Then: get x on one side.
Then: remove the + 20.
Last: check.