Step by step
The question
Question: find x when the angles 3x − 10 and 2x + 20 are complementary.
1 Use the angle fact
Complementary angles add up to 90°.
Together they make a right angle: a corner.
To remember: C comes before S in the alphabet.
90 comes before 180.
So we add the two angles and make it 90: 3x − 10 + 2x + 20 = 90.
Careful!
Complementary means 90, not 180.
180 is for supplementary angles.
2 Group like terms
The x terms go together.
The plain numbers go together.
Now we have 5x + 10 = 90.
3 Remove the + 10
We want 5x 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.
90 minus 10 is 80.
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.
80 divided by 5 is 16.
So x = 16.
5 Check
Let's check: put x = 16 in each angle.
Now add all the angles.
They add up to 90°.
So x = 16 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the + 10.
Then: remove the 5.
Last: check.