The exterior angle of a rectangular polygon is an eighth of interior angle. How many sides does the regular polygon have?
Answers
Step-by-step explanation:
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
Answer by ikleyn(36080) (Show Source): You can put this solution on YOUR website!
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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 = 180%2F9 = 20°.
Thus the interior angle alpha = 8%2Ax = 8%2A20 = 160°.
Now use the formula for the sum of interior angles of n-sided regular polygon.
It gives you an equation to determine n:
n%2Aalpha = 180%2A%28n-2%29, or
n*160 = 180*(n-2).
Simplify and solve it:
160n = 180n - 360 -----> 20n = 360 -----> n = 360%2F20 = 18.
Answer. n = 18.
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