SOLUTION: A regular polygon's interior angle is 8 times as large as its exterior angle

Question 1011166: A regular polygon's interior angle is 8 times as large as its exterior angle
Found 3 solutions by jim_thompson5910, ikleyn, MathTherapy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
E = exterior angle
I = interior angle

I = 8*E since the "interior angle is 8 times as large as its exterior angle"

Each pair of interior and exterior angles add up to 180 degrees
E + I = 180 degrees
E + 8*E = 180 ... replace I with 8E; solve for E
9E = 180
E = 180/9
E = 20

Each exterior angle is 20 degrees

Now let n = number of sides. We can tie n and E together with this formula

E = 360/n

Solve for n to get n = 360/E. Now plug in E = 20

n = 360/E
n = 360/20
n = 18

So there are 18 sides of this polygon.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
A regular polygon's interior angle is 8 times as large as its exterior angle
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Hello,
your posting is not complete! A question is absent.
Therefore, I will add the question instead of you, as I understand it.
The question is: Find the number of sides of the polygon.
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First let us find the interior angle . According to the condition, + = 180�. Hence, + = 180�*8, or = 180�*8, or = = 20�*8 = 160�. Now find n, the number of sides, from the equation = 160, or (n-2)*180 = n*160 -----> (n-2)*9 = n*8, -----> 9n - 18 = 8n -----> 9n - 8n = 18 -----> n = 18. Answer. The number of sides of the regular polygon is 18.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A regular polygon's interior angle is 8 times as large as its exterior angle

If number of sides are required, then read on!
Let number of sides be n
A regular polygon has equal angles and sides
Therefore, one of its exterior angles is: (sum of exterior angles of a polygon is ), and one of its interior angles is:
We then get:

180n � 360 = 2,880 ------ Multiplying by LCD, n
180n = 2,880 + 360
180n = 3,240
n, or number of sides = , or
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