Find the number of sides of a regular polygon if one interior angle is 60 degrees.
A.) 3
B.) 4
C.) 5
D.) 6

Question

Find the number of sides of a regular polygon if one interior angle is 60 degrees.
A.) 3
B.) 4
C.) 5
D.) 6

anonymous · Answer

I'm not so sure how to solve this, can someone please take me through this! :)

mathstudent55 · Answer

Do you know the formula for the sum of the measures of the interior angles of a polygon?

anonymous · Answer

isn't it S= 180(n-2) ?

mathstudent55 · Answer

It is (n - 2)180, where n = number of sides.
Since you have a regular polygon, the measure of each interior angle is the sum of the measures of the angles divided by the number of anlges.

jim_thompson5910 · Answer

If k is the interior angle, then we can use this formula

k = 180(n-2)/n

plug in k = 60 to get

60 = 180(n-2)/n

60n = 180(n-2)

60n = 180n - 360

I'll let you finish in solving for n

mathstudent55 · Answer

That gives you ((n - 2)180) / n,
but this equals 60 in your problem, so you get
((n - 2)180)/n = 60
Now solve the equation for n

anonymous · Answer

I got three when I divided 120 from 360, does that seem right? :O

jim_thompson5910 · Answer

n = 3 is correct

jim_thompson5910 · Answer

here's what it looks like

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anonymous · Answer

that makes a lot more sense!! thank you so much!! :)

jim_thompson5910 · Answer

yw