Step by step
The question
Question: find x when two lines cross and the opposite angles are 4x − 20 and 100°.
1 Use the angle fact
Where two lines cross, the opposite angles are equal.
They are called vertical angles.
So 4x − 20 is the same as 100°: 4x − 20 = 100.
2 Remove the − 20
We want 4x by itself.
The − 20 is in the way.
To remove − 20, we add 20.
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.
− 20 and + 20 make zero.
Cross them out.
100 plus 20 is 120.
3 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
120 divided by 4 is 30.
So x = 30.
4 Check
Let's check: put x = 30 in each angle.
We get 100°, the same as the opposite angle.
So x = 30 is right!
Let's look back.
First: use the angle fact.
Then: remove the − 20.
Then: remove the 4.
Last: check.