Step by step
The question
Question: find x.
The exterior angles of a polygon are 3x + 90, x + 90, 90° 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: 3x + 90 + x + 90 + 90 + 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.
Plain numbers go together.
3x + x = 4x.
90 + 90 + 90 + 90 = 360.
Now we have 4x + 360 = 360.
We want x by itself.
Two things are stuck to x: times 4 and + 360.
The + 360 is on the outside, so it comes off first.
Then the times 4.
3 Remove the + 360
To remove + 360, we take away 360.
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.
+ 360 and − 360 make zero.
Cross them out.
360 − 360 = 0.
Now we have 4x = 0.
4 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
0 divided by 4 is 0.
So x = 0!
5 Check
Let's check: put x = 0 in each angle.
Now add all the angles.
They add up to 360°.
So x = 0 is right!
Let's look back.
First: walk around the shape.
Then: group like terms.
Then: remove the + 360.
Then: remove the 4.
Last: check.