Question 825165
An exterior and and interior angle of a polygon form a linear pair. This makes them are supplementary. So if
x = the smaller angle, then
180 - x =  the larger angle<br>
Then, since the ratio of these is 2:13:
{{{x/(180-x) = 2/13}}}
This can be solved. Cross-multiplying we get:
{{{x*13 = (180-x)2}}}
Simplifying:
{{{13x = 360-2x}}}
Adding 2x:
{{{15x = 360}}}
Dividing by 15:
{{{x = 24}}}
This is the exterior angle. Since the exterior angles add up to 360 and since they are all the same in a regular polygon, the number of exterior angles is:
360/24 = 15.
So the polygon has 15 exterior angles. And since the number of sides is the same as the number of exterior angles, the polygon has 15 sides, a 15-gon.