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anonymous
 one year ago
Find the number of sides of a regular polygon if one interior angle is 120 degrees.
A.) 6
B.) 5
C.) 4
D.) 3
anonymous
 one year ago
Find the number of sides of a regular polygon if one interior angle is 120 degrees. A.) 6 B.) 5 C.) 4 D.) 3

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Do you know the formula that tells you the sum of the measures of the interior angles of a polygon?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Here is the formula: \(S = (n  2)180\) where S = sum of the measures of the interior angles, and n = number of sides.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Do you know what "regular" means when you say regular polygon?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0When all angles are equal?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1It means a polygon that has all sides of the same length and all interior angles of the same measure.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Correct. All angles are congruent, and all sides are congruent.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we can solve this problem. Since you are dealing with a regular polygon, all angles have the same measure. Let's say the sum of the measures of the interior angles is S. Also, let's say your polygon has n sides. Then each angle would have the measure S/n Ok so far?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Just follow what I am explaining . We'll find the answer soon.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1If the sum of the measures of the interior angles is S and the polygon has n sides, then each interior angle measures S/n.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We have a formula for the sum of the measures of the interior angles. \(S = (n  2)180\) If we divide it by n, the number of sides, we will have the measure of one angle. \(\dfrac{S}{n} = \dfrac{(n  2)180}{n} \) is the measure of one angle. We are told one angle measures 120 deg, so we set our expression equal to 120 and ewe solve for n. \(\dfrac{(n  2)180}{n} = 120\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I think I got it now! thank you so much!

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we have to solve that equation for n. We multiply both sides by n: \((n  2)180 = 120n\) Distribute 180 on the left side: \(180n  360 = 120n\) Subtract 120n from both sides, and add 360 to both sides: \(60n = 360\) Divide both sides by 60: \(n = 6\) Since n is the number of sides of the polygon, we can answer: The polygon has 6 sides.
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