Step by step
The question
Question: find x when the angles x and x + 30 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: x + x + 30 = 180.
Careful!
Supplementary means 180, not 90.
90 is for complementary angles.
2 Group like terms
The x terms go together.
Now we have 2x + 30 = 180.
3 Remove the + 30
We want 2x 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 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
150 divided by 2 is 75.
So x = 75.
The angle x is 75°.
5 Check
Let's check: put x = 75 in each angle.
Now add all the angles.
They add up to 180°.
So x = 75 is right!
Let's look back.
First: use the angle fact.
Then: group like terms.
Then: remove the + 30.
Then: remove the 2.
Last: check.