Step by step
The question
Question: find x.
The exterior angles of a polygon are 2x, 2x, 3x, 3x and 90°.
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: 2x + 2x + 3x + 3x + 90 = 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.
2x + 2x + 3x + 3x = 10x.
Now we have 10x + 90 = 360.
We want x by itself.
Two things are stuck to x: times 10 and + 90.
The + 90 is on the outside, so it comes off first.
Then the times 10.
3 Remove the + 90
To remove + 90, we take away 90.
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.
+ 90 and − 90 make zero.
Cross them out.
360 − 90 = 270.
Now we have 10x = 270.
4 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, so they stay equal.
10 divided by 10 is 1.
So just x is left.
270 divided by 10 is 27.
So x = 27!
5 Check
Let's check: put x = 27 in each angle.
Now add all the angles.
They add up to 360°.
So x = 27 is right!
Let's look back.
First: walk around the shape.
Then: group like terms.
Then: remove the + 90.
Then: remove the 10.
Last: check.