Step by step
The question
Question: find x.
The two lines are parallel.
The co-interior angles are 3x − 10 and 2x + 40.
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: 3x − 10 + 2x + 40 = 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.
Plain numbers go together.
3x + 2x = 5x.
−10 + 40 = 30.
Now we have 5x + 30 = 180.
We want x by itself.
Two things are stuck to x: times 5 and + 30.
The + 30 is on the outside, so it comes off first.
Then the times 5.
3 Remove the + 30
To remove + 30, we take away 30.
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.
+ 30 and − 30 make zero.
Cross them out.
180 − 30 = 150.
Now we have 5x = 150.
4 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
150 divided by 5 is 30.
So x = 30!
5 Check
Let's check: put x = 30 in each angle.
Now add the two angles.
They add up to 180°.
So x = 30 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the + 30.
Then: remove the 5.
Last: check.