Step by step
The question
Question: find x when two lines cross and the opposite angles are 5x − 15 and 85°.
1 Use the angle fact
Where two lines cross, the opposite angles are equal.
They are called vertical angles.
So 5x − 15 is the same as 85°: 5x − 15 = 85.
2 Remove the − 15
We want 5x by itself.
The − 15 is in the way.
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 plus 15 is 100.
3 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
100 divided by 5 is 20.
So x = 20.
4 Check
Let's check: put x = 20 in each angle.
We get 85°, the same as the opposite angle.
So x = 20 is right!
Let's look back.
First: use the angle fact.
Then: remove the − 15.
Then: remove the 5.
Last: check.