Step by step
The question
Question: find x.
The exterior angles of a polygon are x, 2x, 3x and 4x.
1 Walk around the shape
Walk along the edge.
At a corner, carry the side on, dashed.
Then turn to the next side.
The turn is the exterior angle.
We turn at every corner.
All the way round, we end up facing the same way as at the start.
That is one full turn.
So the exterior angles add up to 360°.
So we add them all and make it 360: x + 2x + 3x + 4x = 360.
2 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.
x + 2x + 3x + 4x = 10x.
Now we have 10x = 360.
3 Remove the 10
10x means 10 times x.
We want just x.
To remove times 10, we divide by 10.
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.
10 divided by 10 is 1.
So just x is left.
360 divided by 10 is 36.
So x = 36!
4 Check
Let's check: put x = 36 in each angle.
Now add all the angles.
They add up to 360°.
So x = 36 is right!
Let's look back.
First: walk around the shape.
Then: group like terms.
Then: remove the 10.
Last: check.