Worked examples
The question
Question: find the complement of 35°.
We call it x.
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: 35 + x = 90.
35 + x = 90
Careful!
Complementary means 90, not 180.
180 is for supplementary angles.
Careful: not 35 + x = 180 ✗
2 Remove the 35
We want x by itself.
The 35 is in the way.
To remove 35, we take away 35.
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.
35 + x − 35 = 90 − 35
35 and − 35 make zero.
Cross them out.
90 minus 35 is 55.
So x = 55.
The complement of 35° is 55°.
x = 55
3 Check
Let's check: put x = 55 back and add the angles.
35 + 55 = 90
They add up to 90°.
So x = 55 is right!
Let's look back.
First: use the angle fact.
Then: remove the 35.
Last: check.
▶ Watch it solved
The question
Question: find x when the angles x 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 + 2x = 90.
x + 2x = 90
Careful!
Complementary means 90, not 180.
180 is for supplementary angles.
Careful: not x + 2x = 180 ✗
2 Group like terms
The x terms go together.
x + 2x = 3x
Now we have 3x = 90.
3x = 90
3 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.
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.
3x3 = 903
3 divided by 3 is 1.
So just x is left.
90 divided by 3 is 30.
So x = 30.
The angle x is 30°.
x = 30
4 Check
Let's check: put x = 30 in each angle.
2x = 2 × 30 = 60
Now add all the angles.
30 + 60 = 90
They add up to 90°.
So x = 30 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the 3.
Last: check.
▶ Watch it solved
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.
3x − 10 + 2x + 20 = 90
Careful!
Complementary means 90, not 180.
180 is for supplementary angles.
Careful: not 3x − 10 + 2x + 20 = 180 ✗
2 Group like terms
The x terms go together.
The plain numbers go together.
3x + 2x = 5x
-10 + 20 = 10
Now we have 5x + 10 = 90.
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.
5x + 10 − 10 = 90 − 10
+ 10 and − 10 make zero.
Cross them out.
90 minus 10 is 80.
5x = 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.
5x5 = 805
5 divided by 5 is 1.
So just x is left.
80 divided by 5 is 16.
So x = 16.
x = 16
5 Check
Let's check: put x = 16 in each angle.
3x − 10 = 3 × 16 − 10 = 38
2x + 20 = 2 × 16 + 20 = 52
Now add all the angles.
38 + 52 = 90
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.
▶ Watch it solved
