Step by step
The question
Question: find x when the angles x + 15 and 2x 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 + 15 + 2x = 90.
Careful!
Complementary means 90, not 180.
180 is for supplementary angles.
2 Group like terms
The x terms go together.
Now we have 3x + 15 = 90.
3 Remove the + 15
We want 3x by itself.
The + 15 is in the way.
To remove + 15, we take away 15.
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.
+ 15 and − 15 make zero.
Cross them out.
90 minus 15 is 75.
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.
75 divided by 3 is 25.
So x = 25.
5 Check
Let's check: put x = 25 in each angle.
Now add all the angles.
They add up to 90°.
So x = 25 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the + 15.
Then: remove the 3.
Last: check.