1 solution; Let each inner angle be x degrees and the adjacent outer angle be y degrees, so:

x+y= 180

x=y

Solution: x=90, y=90,

The sum of the outer angles of the multilateral rows is 360 degrees.

360÷90=4

Answer: This polygon is a square, and each outer angle is 90 degrees.

2 Solution: If each external angle of a polygon is equal to one-fifth of the adjacent internal angle, that is, each internal angle is five times the degree of the adjacent internal angle, then the degree of each external angle is:

180(5+ 1)= 30 (degrees);

The sum of the external angles is 360 degrees, so the number of sides of this polygon is:

360÷30= 12 (articles).

So such a polygon exists, and it is a dodecagon.

Every time the number of sides of a polygon increases, the sum of its internal angles increases by 180 degrees; The sum of the outer angles of a polygon is a constant value, that is, the sum of the outer angles of a polygon is always 360 degrees.