Find the number of sides of a regular polygon whose outer angle is 60?

First, let’s determine what the inner angle of the specified polygon will be equal to, because from the condition of this task we know that its outer angle is 60 °:

180 – 60 = 120.

Now we can determine how many sides a given regular polygon has, for which we use the formula well-known from the school curriculum in geometry:

аn = 180 ° * (m – 2): m;

120 = 180 (m – 2): m;

120m = 180m – 360;

-60m = -360;

m = 6.

Answer: This polygon has 6 sides.