Question 242890
Well regular means that the polgon has equal interior angles. The formula for the interior angle of a regular polygon is {{{((n-2)*180)/n}}} where n is the number of sides.

So we know the interior angle is 174 and we need to find out what n is.

{{{174 =(180n-360)/n}}}
{{{174 =180-360/n}}}
{{{-6=-360/n}}}
{{{-360/-6=n}}}

So n = 60

Does that makes sense?