Question 1059474
All the exterior angles add to 360 degrees
Therefore, if one polygon's exterior angle is x, and the other ix x-21, we have 360/x and 360/(x-21) as the number of sides
(360/x)=number of sides with the polygon with fewer sides
360/(x-21)=number of sides with the polygon with more sides.  The denominator is smaller so the value is greater.  For example, if x=24, one polygon would have 15 sides and the other would have 120
(360/x)+14=360/(x-21)
Multiply everything by x(x-21)
360(x-21)+14x^2-294x=360x
360x-7560+14x^2-294x=360x
14x^2-294x-7560=0
divide by 14, since all are evenly divisible
x^2-21x-540=0
(x-36)(x+15)=0
x=36 as only reasonable root.
One polygon has 36 sides and an exterior angle of 360/36=10 degrees.
The other polygon has 15 sides and an exterior angle of 360/15=24 degrees.  That difference is 14 degrees.