Question

A regular polygon has a exterior of 18 degrees. How many sides does it have?

Answer 1

The angles of a regular polygon add up to 360 degrees so if it is a REGULAR polygon then all of the angles must be equal/the same. So you do 360 divided by 18 to see how many sides there are so that would give a simple answer of 20. I was able to work this out in my head by doing 36 divided 18 (I took the 0 off the 360 to make the sum easier) which = 2 and then added the 0 back on from the 360 which gave me 20. So the regular polygon has 20 sides

Answer 2

The formula of the measurement of an exterior angle of a regular polygon is
β = 360°/n
where β = exterior angle and n = number of sides

Therefore,
n = 360°/β = 360°/18° = 20 sides