Question 377945
Recall that the formula for the sum of the measures in a convex polygon with n sides is

{{{S = 180(n-2)}}}

When the polygon is regular, all of its angles are equal so to find the measure of one interior angle, we divide by n:
{{{175 = 180(n-2)/n}}}

Solving, we have {{{175n = 180n - 360}}} --> 5n = 360 --> n = 72. This is an integer, so a regular polygon with 72 sides would have interior angles measuring 175 degrees.