Step by step
The question
Question: find x when the angles x and 48° 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: x + 48 = 90.
Careful!
Complementary means 90, not 180.
180 is for supplementary angles.
2 Remove the + 48
We want x by itself.
The + 48 is in the way.
To remove + 48, we take away 48.
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.
+ 48 and − 48 make zero.
Cross them out.
90 minus 48 is 42.
So x = 42.
The angle x is 42°.
3 Check
Let's check: put x = 42 back and add the angles.
They add up to 90°.
So x = 42 is right!
Let's look back.
First: use the angle fact.
Then: remove the + 48.
Last: check.