Lots and lots and lots. When you think the angle is nearly 180 degrees or a straight line, it must have lots and lots of sides.
The total of the interior angles of a polygon is given by (n-2)180, so the angle of each interior angle of a regular polygon is given by ((n-2)180)/n.
Now we set this to be equal to 176 and solve for n.
(n-2)180 = 176
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n
Multiplying both sides by n, we get (n-2) 180 = 176n
Expanding the left side of the equation, 180n - 360 = 176n
Subtracting 176n from both sides and adding 360 to both sides, we get
180n - 176n = 360
4n = 360
Dividing both sides by 4, n = 90
Thus, you need a regular polygon of 90 sides to get an internal angle of 176 degrees.
Hopefully you don't have to construct it.
Good luck,
Paul
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