Step by step
The question
Question: find x.
The two lines are parallel.
The corresponding angles are x + 80 and 65°.
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: x + 80 = 65.
2 Remove the + 80
We want x by itself.
The + 80 is in the way.
To remove + 80, we take away 80.
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.
+ 80 and − 80 make zero.
Cross them out.
65 − 80 = −15.
So x = −15!
3 Check
Let's check: put x = −15 in each angle.
We get 65°, the same as the other angle.
So x = −15 is right!
Let's look back.
First: use the angle fact.
Then: remove the + 80.
Last: check.