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Mathematics
OpenStudy (anonymous):

Please help... Each interior angle of a regular polygon is p times each exterior angle. Find an expression in terms of p for (1) an exterior angle (2) the number of sides of the polygon

OpenStudy (ash2326):

Let each interior angle be A And each exterior angle be B It's given that each interior angle is p time the exterior angle. \[A=p\times B\] We know for a regular polygon exterior angle + interior angle=180 so \[A+B=180\] A=pB so \[pB+B=180\] or \[B(p+1)=180\] or exterior angle B \[B=\frac{180}{p+1}\] First part solved

OpenStudy (anonymous):

Got it! Thank you! :) What about second part?

OpenStudy (ash2326):

Now interior angle A for a regular polygon with n sides \[A=(n-2)\frac{180}{n}\] so \[nA=(n-2) \times 180\] or \[nA-180n=-360\] or \[n(A-180)=-360\] or \[n=\frac{360}{180-A}\] 180-A=B \[n=\frac{360}{B}\] and pB=A or B=A/p so \[n=\frac{360p}{A}\]

OpenStudy (anonymous):

Thank you so much for answering this! :)

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