Step by step
The question
Question: find x.
The two lines are parallel.
The co-interior angles are 2x and 100°.
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: 2x + 100 = 180.
We want x by itself.
Two things are stuck to x: times 2 and + 100.
The + 100 is on the outside, so it comes off first.
Then the times 2.
2 Remove the + 100
To remove + 100, we take away 100.
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.
+ 100 and − 100 make zero.
Cross them out.
180 − 100 = 80.
Now we have 2x = 80.
3 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
80 divided by 2 is 40.
So x = 40!
4 Check
Let's check: put x = 40 in each angle.
Now add the two angles.
They add up to 180°.
So x = 40 is right!
Let's look back.
First: use the angle fact.
Then: remove the + 100.
Then: remove the 2.
Last: check.