\begin{tabular}{l} Question 4 \ The size of each interior angle of a regular polygon is $$ 165^{\circ} $$. How many sides does the polygon have? \ $$ \begin{array}{l}24 \ 22 \ 20 \ 26\end{array} $$ \ \hline\end{tabular}

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To find the number of sides of a regular polygon given that each interior angle is $$ 165^\circ $$, we can use the formula for the interior angle of a regular polygon:

$$
\text{Interior angle} = \frac{(n-2) \times 180^\circ}{n}
$$

where $$ n $$ is the number of sides of the polygon. Setting the interior angle equal to $$ 165^\circ $$, we have:

$$
\frac{(n-2) \times 180^\circ}{n} = 165^\circ
$$

To eliminate the fraction, we can multiply both sides by $$ n $$:

$$
(n-2) \times 180 = 165n
$$

Expanding the left side:

$$
180n - 360 = 165n
$$

Now, we can isolate $$ n $$ by moving all terms involving $$ n $$ to one side:

$$
180n - 165n = 360
$$

This simplifies to:

$$
15n = 360
$$

Now, divide both sides by $$ 15 $$:

$$
n = \frac{360}{15} = 24
$$

Thus, the polygon has $$ 24 $$ sides.

The answer is $$ \boxed{24} $$.
The polygon has 24 sides.

Question 4

The size of each interior angle of a regular polygon is . How many sides does the polygon have?

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Question 4 The size of each interior angle of a regular polygon is . How many sides does the polygon have?