Step by step
The question
Question: find x.
The two lines are parallel.
The corresponding angles are 2x − 15 and 85°.
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 − 15 = 85.
We want x by itself.
Two things are stuck to x: times 2 and − 15.
The − 15 is on the outside, so it comes off first.
Then the times 2.
2 Remove the − 15
To remove − 15, we add 15.
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.
− 15 and + 15 make zero.
Cross them out.
85 + 15 = 100.
Now we have 2x = 100.
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.
100 divided by 2 is 50.
So x = 50!
4 Check
Let's check: put x = 50 in each angle.
We get 85°, the same as the other angle.
So x = 50 is right!
Let's look back.
First: use the angle fact.
Then: remove the − 15.
Then: remove the 2.
Last: check.