Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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

61 PointsDETAILSALEXGEOM7 83006MY NOTESASK YOUR TEACHERIn A Regular Polygon Each Interior Angle Measures 120 If Each Side Of The Regular Polygon Measures 46 Cm class=

Sagot :

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

Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.