Step by step
The question
Question: find x.
The angles of a hexagon are 120°, 130°, 110°, 125°, 140° and x.
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: 120 + 130 + 110 + 125 + 140 + 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.
120 + 130 + 110 + 125 + 140 = 625.
Now we have 625 + x = 720.
4 Remove the 625
We want x by itself.
The 625 is in the way.
To remove 625, we take away 625.
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.
625 and − 625 make zero.
Cross them out.
720 − 625 = 95.
So x = 95!
5 Check
Let's check: put x = 95 back and add the angles.
They add up to 720°.
So x = 95 is right!
Let's look back.
First: find the angle sum.
Then: use the angle fact.
Then: group like terms.
Then: remove the 625.
Last: check.