Step by step
The question
Question: find x.
The angles of a pentagon are 100°, 120°, 95°, 110° 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: 100 + 120 + 95 + 110 + 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.
100 + 120 + 95 + 110 = 425.
Now we have 425 + x = 540.
4 Remove the 425
We want x by itself.
The 425 is in the way.
To remove 425, we take away 425.
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.
425 and − 425 make zero.
Cross them out.
540 − 425 = 115.
So x = 115!
5 Check
Let's check: put x = 115 back and add the angles.
They add up to 540°.
So x = 115 is right!
Let's look back.
First: find the angle sum.
Then: use the angle fact.
Then: group like terms.
Then: remove the 425.
Last: check.