Question 1012114: In a regular polygon, the exterior angle is one-eighth of an interior angle. How many sides has the polygon? Found 3 solutions by Boreal, ikleyn, MathTherapy:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! {(n-2)/n}*180 is interior angle
exterior angle is 1/8 of that or {(n-2)/n}*22.5
The two add to 180
[180n-360]/n +[22.5n-45]/n=180
multiply by n
180n-360+22.5n-45=180n
22.5 n=405
n=18
18 sides
You can put this solution on YOUR website! .
In a regular polygon, the exterior angle is one-eighth of an interior angle. How many sides has the polygon?
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First, let us find the interior angle.
Let x be the exterior angle. Then the interior angle is 8x.
Their sum is 180°. It gives you an equation
x + 8x = 180, or 9x = 180, or x = = 20°.
Thus the interior angle = = = 160°.
Now use the formula for the sum of interior angles of n-sided regular polygon.
It gives you an equation to determine n:
= , or
n*160 = 180*(n-2).
Simplify and solve it:
160n = 180n - 360 -----> 20n = 360 -----> n = = 18.
Answer. n = 18.
You can put this solution on YOUR website!
In a regular polygon, the exterior angle is one-eighth of an interior angle. How many sides has the polygon?
Let one of the exterior angles, be E
Then one of the interior angles = 8E
Since both sum to , we get: E + 8E = 180
9E = 180
E, or one of the exterior angles = , or
Since the sum of the exterior angles of a polygon is , and with one exterior
angle of the REGULAR polygon being , number of sides = , or
