Step by step
The question
Question: find x.
The angles of a pentagon are 2x, 3x, 100°, 120° and 140°.
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: 2x + 3x + 100 + 120 + 140 = 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.
2x + 3x = 5x.
100 + 120 + 140 = 360.
Now we have 5x + 360 = 540.
We want x by itself.
Two things are stuck to x: times 5 and + 360.
The + 360 is on the outside, so it comes off first.
Then the times 5.
4 Remove the + 360
To remove + 360, we take away 360.
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.
+ 360 and − 360 make zero.
Cross them out.
540 − 360 = 180.
Now we have 5x = 180.
5 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.
5 divided by 5 is 1.
So just x is left.
180 divided by 5 is 36.
So x = 36!
6 Check
Let's check: put x = 36 in each angle.
Now add all the angles.
They add up to 540°.
So x = 36 is right!
Let's look back.
First: find the angle sum.
Then: use the angle fact.
Then: group like terms.
Then: remove the + 360.
Then: remove the 5.
Last: check.