Step by step
The question
Question: find x.
The angles of a pentagon are 108°, 112°, 90°, 130° and x.
1 Find the angle sum
Pick one corner.
Draw lines from it to the other corners.
They cut the pentagon into 3 triangles.
There are always 2 fewer triangles than sides: 5 − 2 = 3.
Each triangle has 180°.
3 times 180 is 540.
2 Use the angle fact
The angles of the pentagon add up to 540°.
So we add them all and make it 540: 108 + 112 + 90 + 130 + x = 540.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
108 + 112 + 90 + 130 = 440.
Now we have 440 + x = 540.
4 Remove the 440
We want x by itself.
The 440 is in the way.
To remove 440, we take away 440.
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.
440 and − 440 make zero.
Cross them out.
540 − 440 = 100.
So x = 100!
5 Check
Let's check: put x = 100 back and add the angles.
They add up to 540°.
So x = 100 is right!
Let's look back.
First: find the angle sum.
Then: use the angle fact.
Then: group like terms.
Then: remove the 440.
Last: check.