Step by step
The question
Question: find x when the angles 4x and 5x are supplementary.
1 Use the angle fact
Supplementary angles add up to 180°.
Together they make a straight line.
To remember: C comes before S in the alphabet.
90 comes before 180.
So we add the two angles and make it 180: 4x + 5x = 180.
Careful!
Supplementary means 180, not 90.
90 is for complementary angles.
2 Group like terms
The x terms go together.
Now we have 9x = 180.
3 Remove the 9
9x means 9 times x.
We want just x.
To remove times 9, we divide by 9.
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.
9 divided by 9 is 1.
So just x is left.
180 divided by 9 is 20.
So x = 20.
4 Check
Let's check: put x = 20 in each angle.
Now add all the angles.
They add up to 180°.
So x = 20 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the 9.
Last: check.