Step by step
The question
Question: find x.
The angles of a pentagon are x + 20, x − 10, 2x, 110° and 100°.
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: x + 20 + x − 10 + 2x + 110 + 100 = 540.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
Plain numbers go together.
x + x + 2x = 4x.
20 − 10 + 110 + 100 = 220.
Now we have 4x + 220 = 540.
We want x by itself.
Two things are stuck to x: times 4 and + 220.
The + 220 is on the outside, so it comes off first.
Then the times 4.
4 Remove the + 220
To remove + 220, we take away 220.
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.
+ 220 and − 220 make zero.
Cross them out.
540 − 220 = 320.
Now we have 4x = 320.
5 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
320 divided by 4 is 80.
So x = 80!
6 Check
Let's check: put x = 80 in each angle.
Now add all the angles.
They add up to 540°.
So x = 80 is right!
Let's look back.
First: find the angle sum.
Then: use the angle fact.
Then: group like terms.
Then: remove the + 220.
Then: remove the 4.
Last: check.