Step by step
The question
Question: find x.
The exterior angles of a polygon are 100°, 80°, 75°, 60° and x.
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: 100 + 80 + 75 + 60 + x = 360.
2 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.
100 + 80 + 75 + 60 = 315.
Now we have 315 + x = 360.
3 Remove the 315
We want x by itself.
The 315 is in the way.
To remove 315, we take away 315.
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.
315 and − 315 make zero.
Cross them out.
360 − 315 = 45.
So x = 45!
4 Check
Let's check: put x = 45 back and add the angles.
They add up to 360°.
So x = 45 is right!
Let's look back.
First: walk around the shape.
Then: group like terms.
Then: remove the 315.
Last: check.