3. Number of sides in a regular polygon with an interior angle of $$ 175.2^{\circ} $$

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1. The formula for an interior angle $$ A $$ of a regular polygon with $$ n $$ sides is
   $$
   A = \frac{(n-2) \cdot 180}{n}.
   $$
2. Given that $$ A = 175.2^\circ $$, substitute into the equation:
   $$
   175.2 = \frac{(n-2) \cdot 180}{n}.
   $$
3. Multiply both sides by $$ n $$ to eliminate the fraction:
   $$
   175.2n = 180(n-2).
   $$
4. Expand the right-hand side:
   $$
   175.2n = 180n - 360.
   $$
5. Rearrange the equation to isolate the terms involving $$ n $$:
   $$
   180n - 175.2n = 360.
   $$
6. Combine like terms:
   $$
   4.8n = 360.
   $$
7. Solve for $$ n $$:
   $$
   n = \frac{360}{4.8} = 75.
   $$

The regular polygon has $$ 75 $$ sides.
A regular polygon with an interior angle of $$ 175.2^\circ $$ has 75 sides.

Number of sides in a regular polygon
with an interior angle of

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