Question 1152296
each exterior angle in a regular polygon is equal to 180 minus the interior angle.
that makes the exterior angle equal to 180 - 176 = 4 degrees.
the number of sides in the regular polygon is equal to 360 divided by the number of degrees in the exterior angle.
that makes the number of side equal to 360 / 4 = 90.


the formula based on the interior angle is:
i = 180 * (n - 2) / n
i is the measure of the interior angle
n is the number of sides.
the formula becomes:
176 = 180 * (n - 2) / n
multiply both sides by n and simplify to get:
176 * n = 180 * n - 360
add 360 to both sides of this equation and subtract 176 * n from both sides of this equation to get:
360 = 180 * n - 176 * n
combine like terms to get:
360 = 4 * n
solve for n to get n = 360 / 4 = 90


your solution is that the number of side of the regular polygon is 90.