Question 745457
In a regular polygon each interior angle is 140 degrees greater than each exterior angle. Calculate the number of sides of the polygon. How can i solve this?

Let
i is the interior angle
e is the exterior angle
n is the number of sides

The formula:
{{{i=180(n-2)/n}}}  {{{equation 1}}}
{{{e=360/n}}} {{{equation 2}}}
"...interior angle is 140 degrees greater than each exterior angle..."
{{{i=e+140}}} {{{equation 3}}}
Substitute equation 1 and 2 to equation 3
{{{180(n-2)/n=360/n+140}}}
{{{720=40n}}}
{{{n=18}}}