Let the number of sides of this polygon be n, and the sum of its internal angles = (n-3) * 180.

Let the vertex of this angle be A, and its two adjacent vertices are B and C, extending slightly from CA to D.

That is, ∠BAC is the inner corner ∠BAD is the outer corner.

Connect B and C to divide the original polygon into a triangle and a polygon with n- 1 sides.

Therefore: (n-1-3) *180+∠ bad+∠ ABC+∠ ACB = 600.

And ∠BAD=∠ABC+∠ACB.

So: (n-4) * 180+2 * ∠ bad = 600.

Because: 0 < 2 * ∠ bad < 360.

Therefore: 600-360 < (n-4) * 180 < 600.

So: 1.3 < n-4 < 3.4.

So: n = 6,7

When n=6, the external angle ∠ bad = 120.

When n = 7°, the external angle ∠ bad = 30.