Question 1011166
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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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<pre>
First let us find the interior angle {{{alpha}}}. 
According to the condition, 

{{{alpha/8}}}  + {{{alpha}}} = 180°.

Hence, {{{alpha}}} + {{{8*alpha}}} = 180°*8,  or  {{{9*alpha}}} = 180°*8,  or  {{{alpha}}} = {{{(180^o*8)/9}}} = 20°*8 = 160°.

Now find n, the number of sides, from the equation

{{{((n-2)*180)/n}}} = 160,  or


(n-2)*180 = n*160  -----> (n-2)*9 = n*8,  -----> 9n - 18 = 8n  -----> 9n - 8n = 18  -----> n = 18.

<U>Answer</U>. The number of sides of the regular polygon is 18.
</pre>