Find the number of sides of a regular polygon if each interior angle is 165°.

Correct option is A

Given:
Each interior angle of the regular polygon is 165^\circ .

Formula Used:
The formula for the interior angle A of a regular polygon with n sides is:
$$A = \frac{(n - 2) \times 180}{n}$$​}
where:
- A is the measure of each interior angle,
- n is the number of sides of the polygon.

Solution:

Substitute A = 165 into the formula:
​$$165 = \frac{(n - 2) \times 180}{n}$$​​

Multiply both sides by n :
​$$165n = (n - 2) \times 180$$​​

Expand and rearrange to solve for n :
165n = 180n - 360
180n - 165n = 360
15n = 360

Divide both sides by 15:
​$$n = \frac{360}{15}\\\ \\n = 24$$​​

The regular polygon has 24 sides.

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