Question

the interior angles of an n-gon have an average measure of $120^{\circ}$. what is n?
select the correct answer below and, if necessary, fill in the answer box to complete your choice.
a. $n=\square$ (simplify your answer )
b. there is no such polygon

Explanation:

Step1: Recall total interior angles formula

The sum of interior angles of an n-gon is $(n-2)\times180^\circ$.

Step2: Set up average angle equation

Average angle = $\frac{\text{Total interior angles}}{n}$, so:
$$120^\circ = \frac{(n-2)\times180^\circ}{n}$$

Step3: Solve for n

Multiply both sides by $n$:
$$120n = 180(n-2)$$
Expand right side:
$$120n = 180n - 360$$
Rearrange terms:
$$360 = 180n - 120n$$
$$360 = 60n$$
$$n = \frac{360}{60} = 6$$

Answer:

A. $n=6$