Step by step
The question
Question: find x.
The angles of a hexagon are x, x, 2x, 2x, 120° and 120°.
1 Find the angle sum
Pick one corner.
Draw lines from it to the other corners.
They cut the hexagon into 4 triangles.
There are always 2 fewer triangles than sides: 6 − 2 = 4.
Each triangle has 180°.
4 times 180 is 720.
2 Use the angle fact
The angles of the hexagon add up to 720°.
So we add them all and make it 720: x + x + 2x + 2x + 120 + 120 = 720.
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 + 2x = 6x.
120 + 120 = 240.
Now we have 6x + 240 = 720.
We want x by itself.
Two things are stuck to x: times 6 and + 240.
The + 240 is on the outside, so it comes off first.
Then the times 6.
4 Remove the + 240
To remove + 240, we take away 240.
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.
+ 240 and − 240 make zero.
Cross them out.
720 − 240 = 480.
Now we have 6x = 480.
5 Remove the 6
6x means 6 times x.
We want just x.
To remove times 6, we divide by 6.
We do it on both sides, so they stay equal.
6 divided by 6 is 1.
So just x is left.
480 divided by 6 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 720°.
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 + 240.
Then: remove the 6.
Last: check.