Step by step
The question
Question: find x.
The two lines are parallel.
The corresponding angles are 3x and 105°.
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: 3x = 105.
2 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
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.
3 divided by 3 is 1.
So just x is left.
105 divided by 3 is 35.
So x = 35!
3 Check
Let's check: put x = 35 in each angle.
We get 105°, the same as the other angle.
So x = 35 is right!
Let's look back.
First: use the angle fact.
Then: remove the 3.
Last: check.