Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A 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

We hope this was helpful. Please come back whenever you need more information or answers to your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.