Question

6.[–/1 Points]DETAILSALEXGEOM7 8.3.006.MY NOTESASK YOUR TEACHERIn a regular polygon, each interior angle measures 120°. If each side of the regular polygon measures 4.6 cm, find the perimeter of the polygon in centimeters. cm

Answer 1

Given:

Measure of each interior angle = 120 degrees

Length of each side = 4.6 cm

Let's find the perimeter of the polygon.

Since the measure of each interior angle is 120 degrees, let's find the number of sides of the polygon using the formula below:

$120=\frac{(n-2)*180}{n}$

Let's solve for n.

We have:

$\begin{gathered} 120n=(n-2)*180 \\ \\ 120n=180n-180(2) \\ \\ 120n=180n-360 \\ \\ 180n-120n=360 \\ \\ 60n=360 \end{gathered}$

Divide both sides by 60:

$\begin{gathered} \frac{60n}{60}=\frac{360}{60} \\ \\ n=6 \end{gathered}$

Therefore, the polygon has 6 sides.

To find the perimeter, apply the formula:

Perimeter = number of sides x length of each side

Perimeter = 6 x 4.6

Perimeter = 27.6 cm

Therefore, the perimeter of the polygon is 27.6 cm

ANSWER:

27.6 cm