Given options for exterior angles are 30°, 36°, 45°, 50° we know that sum of all exterior angles in a regular polygon = 180° now, individual exterior angle in regular polygon = $$frac{180}{n}$$ where , n = number of sides in a polygon. and hence we can say n should be a positive integer as number of sides can not be in fraction or negative . Now start, checking given angles. If exterior angle is 30° , then number of sides = $$frac{180}{30}$$ = 6 If exterior angle is 36° , then number of sides = $$frac{180}{36}$$ = 5 If exterior angle is 45° , then number of sides = $$frac{180}{45}$$ = 4
If exterior angle is 50° , then number of sides = $$frac{180}{50}$$ = $$frac{18}{5}$$ as one can see that in last option of exterior angle 50°, number of sides is coming in fraction and hence this option is not valid.