Step by step
The question
Question: find x.
The two lines are parallel.
The corresponding angles are 2x + 25 and 4x − 15.
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 + 25 = 4x − 15.
2 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 2x from the left side.
To remove 2x, we take away 2x.
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.
2x and − 2x make zero.
Cross them out.
4x − 2x = 2x.
Now we have 25 = 2x − 15.
Let's swap the two sides, so x is on the left.
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.
3 Remove the − 15
To remove − 15, we add 15.
We do it on both sides, so they stay equal.
− 15 and + 15 make zero.
Cross them out.
25 + 15 = 40.
Now we have 2x = 40.
4 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.
40 divided by 2 is 20.
So x = 20!
5 Check
Let's check: put x = 20 in each angle.
Both angles are 65°.
They are equal, so x = 20 is right!
Let's look back.
First: use the angle fact.
Then: get x on one side.
Then: remove the − 15.
Then: remove the 2.
Last: check.