$$ 180-A=\frac{360}{n} $$

The measure \(A\) in degrees, of an interior angle of a regular polygon is related to the number of sides, \(n\), of the polygon by the formula above. If the measure of an interior angle of a regular polygon is less than \(120\degree\), what is the greatest number of sides it can have?

Summary Submit Skip Question

We are told the interior angle \(A\) is less than \(40 \degree\):

$$ A \lt 120 \degree $$

We can use the given equation. Solving for \(A\) allows us to substitute it into the inequality.

$$ 180-A=\frac{360}{n} $$ $$ A=180-\frac{360}{n} $$ $$ 180-\frac{360}{n} \lt 120 $$

Solving for n:

$$ \frac{360}{n} \gt 60 $$ $$ 360 \gt 60n $$ $$ n \lt 6 $$ $$ n=\boxed{5} $$