Step by step
The question
Question: find x.
The two lines are parallel.
The corresponding angles are 5x + 5 and 110°.
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: 5x + 5 = 110.
We want x by itself.
Two things are stuck to x: times 5 and + 5.
The + 5 is on the outside, so it comes off first.
Then the times 5.
2 Remove the + 5
To remove + 5, we take away 5.
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.
+ 5 and − 5 make zero.
Cross them out.
110 − 5 = 105.
Now we have 5x = 105.
3 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.
105 divided by 5 is 21.
So x = 21!
4 Check
Let's check: put x = 21 in each angle.
We get 110°, the same as the other angle.
So x = 21 is right!
Let's look back.
First: use the angle fact.
Then: remove the + 5.
Then: remove the 5.
Last: check.