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:
[tex]120=\frac{(n-2)*180}{n}[/tex]
Let's solve for n.
We have:
[tex]\begin{gathered} 120n=(n-2)*180 \\ \\ 120n=180n-180(2) \\ \\ 120n=180n-360 \\ \\ 180n-120n=360 \\ \\ 60n=360 \end{gathered}[/tex]
Divide both sides by 60:
[tex]\begin{gathered} \frac{60n}{60}=\frac{360}{60} \\ \\ n=6 \end{gathered}[/tex]
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
