Question

How many sides does a regular polygon have if each of the interior angles is \[{60^\circ}\]?

Answer 1

Hint: A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of all angles of a regular polygon having n sides = 180 (n-2). To find the measure of one interior angle, we take that formula and divide by the number of sides n: \[\dfrac{{180(n - 2)}}{n}\].

Complete step-by-step answer:
From the above explanation we get:
\[ \Rightarrow \dfrac{{180(n - 2)}}{n} = {60^\circ}\]
\[
  180n - {360^\circ} = 60n \\
  120n = {360^\circ} \\
  n = 3 \\
\]
Number of sides = 3

Note: While solving this problem one should know the basic simple formula to calculate the sides of a polygon from its angle given. It is wise to remember such formulas as it will help us to solve the problem quickly and it will not consume much time.