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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