The sum of the interior angles of a polygon: =(n-2)* 180, so (n-2) * 180- (an interior angle)+(an exterior angle) =600 degrees.

Internal angle+external angle = 180 degrees.

Substitution simplification gives: (n-2)* 180-( 180- external angle)+external angle =600.

Therefore: (n-3)* 180+2 external angle =600 (n is greater than 3), n is less than or equal to 6, 180 degrees = =30 degrees.

When n is 6, the external angle is 30 degrees, when n is 5, the external angle is 120 degrees, and when n is 4, the external angle is 2 10 degrees, which is wrong and untenable.

So there are two situations: n is 6 and the outer angle is 30 degrees; N is 5, and the external angle is 120 degrees.