Step by step
The question
Question: find x.
The angles of a hexagon are 110°, 125°, 130°, 115°, 120° and x.
1 Find the angle sum
Pick one corner.
Draw lines from it to every corner that is not next to it.
They cut the hexagon into 4 triangles.
The two sides at our corner get no triangle of their own.
So there are 2 fewer triangles than sides: 6 − 2 = 4.
Each triangle has 180°: 4 × 180.
180 is 18 tens.
So forget the zero: 4 times 18 is 72.
Put the zero back: 720.
So the angle sum 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: 110 + 125 + 130 + 115 + 120 + x = 720.
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.
110 + 125 + 130 + 115 + 120 = 600.
Now we have 600 + x = 720.
Is x alone now?
Not yet: + 600 is still with x.
How do we remove it?
4 Remove the 600
We want x by itself.
The 600 is in the way.
To remove 600, we take away 600.
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.
600 and − 600 cancel each other.
They make zero.
720 − 600 = 120.
So x = 120!
5 Check
Let's check: put x = 120 back and add the angles.
They add up to 720°.
So x = 120 is right!
Let's look back.
First: find the angle sum.
Then: use the angle fact.
Then: group like terms.
Then: remove the 600.
Last: check.