Step by step
The question
Question: find x when two lines cross and the opposite angles are 3x + 10 and 70°.
1 Use the angle fact
Where two lines cross, the opposite angles are equal.
They are called vertical angles.
So 3x + 10 is the same as 70°: 3x + 10 = 70.
2 Remove the + 10
We want 3x by itself.
The + 10 is in the way.
To remove + 10, we take away 10.
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.
+ 10 and − 10 make zero.
Cross them out.
70 minus 10 is 60.
3 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, so they stay equal.
3 divided by 3 is 1.
So just x is left.
60 divided by 3 is 20.
So x = 20.
4 Check
Let's check: put x = 20 in each angle.
We get 70°, the same as the opposite angle.
So x = 20 is right!
Let's look back.
First: use the angle fact.
Then: remove the + 10.
Then: remove the 3.
Last: check.