Question

Work out the number of sides of a regular polygon with the interior angle of 172 degrees.

Answer 1

$interior\ angle=\frac{(n-2)*180}{n}\\n-number\ of\ sides\\\\ 172=\frac{(n-2)*180}{n}\ \ \ |*n\\ 172n=180n-360\ \ \ |Subtract\ 180n\\ -8n=-360\ \ \ |Divide\ by\ -8\\ n=45\\\\ Number\ of\ side\ is\ equal\ to\ 45.$