First, let us find the interior angle.
Let x be the exterior angle. Then the interior angle is 8x.

Their sum is 180°. It gives you an equation

x + 8x = 180,   or   9x = 180,   or x =  = 20°.

Thus the interior angle  =  =  = 160°.

Now use the formula for the sum of interior angles of n-sided regular polygon.
It gives you an equation to determine n:

 = ,   or

n*160 = 180*(n-2).

Simplify and solve it:

160n = 180n - 360  ----->   20n = 360  ----->   n =  = 18.

Answer. n = 18.

Let one of the exterior angles, be E

Then one of the interior angles = 8E

Since both sum to , we get: E + 8E = 180

9E = 180

E, or one of the exterior angles = , or 

Since the sum of the exterior angles of a polygon is , and with one exterior

angle of the REGULAR polygon being , number of sides = , or  

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