Step by step
The question
Question: find x when the angles on a straight line are x + 20 and 2x + 10.
1 Use the angle fact
Angles on a straight line add up to 180°.
A straight line is half a turn.
So we add them all and make it 180: x + 20 + 2x + 10 = 180.
2 Group like terms
The x terms go together.
The plain numbers go together.
Now we have 3x + 30 = 180.
3 Remove the + 30
We want 3x by itself.
The + 30 is in the way.
To remove + 30, we take away 30.
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.
+ 30 and − 30 make zero.
Cross them out.
180 minus 30 is 150.
4 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.
150 divided by 3 is 50.
So x = 50.
5 Check
Let's check: put x = 50 in each angle.
Now add all the angles.
They add up to 180°.
So x = 50 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the + 30.
Then: remove the 3.
Last: check.