Step by step
The question
Question: find x.
The two lines are parallel.
The co-interior angles are 4x and 5x.
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 between the parallel lines, on the same side of the transversal.
They are called co-interior angles, or same-side interior angles.
Together they make a C shape.
Co-interior angles add up to 180°.
Why?
Look at this angle at the top.
It is in the same place as the bottom angle, so they are equal.
With our top angle, it makes a straight line: 180°.
Careful: they are not equal.
They add up to 180°.
So we add them and make it 180: 4x + 5x = 180.
2 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
4x + 5x = 9x.
Now we have 9x = 180.
3 Remove the 9
9x means 9 times x.
We want just x.
To remove times 9, we divide by 9.
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.
9 divided by 9 is 1.
So just x is left.
180 divided by 9 is 20.
So x = 20!
4 Check
Let's check: put x = 20 in each angle.
Now add the two angles.
They add up to 180°.
So x = 20 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the 9.
Last: check.