Step by step
The question
Question: find x when the angles 2x + 40 and 3x − 10 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: 2x + 40 + 3x − 10 = 180.
Careful!
Supplementary means 180, not 90.
90 is for complementary angles.
2 Group like terms
The x terms go together.
The plain numbers go together.
Now we have 5x + 30 = 180.
3 Remove the + 30
We want 5x 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 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.
150 divided by 5 is 30.
So x = 30.
5 Check
Let's check: put x = 30 in each angle.
Now add all the angles.
They add up to 180°.
So x = 30 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the + 30.
Then: remove the 5.
Last: check.