We are given that each interior angle of a regular polygon is $168^{\circ}$. We need to find the number of sides of the polygon.

1. Problem Description

We are given that each interior angle of a regular polygon is $168^{\circ}$. We need to find the number of sides of the polygon.

2. Solution Steps

Let $n$ be the number of sides of the regular polygon.

The measure of each interior angle of a regular $n$-sided polygon is given by the formula:

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

We are given that the interior angle is $168^{\circ}$. So we have:

$$\frac{(n-2) \times 180}{n} = 168$$

Multiply both sides by $n$:

$$(n-2) \times 180 = 168n$$

$$180n - 360 = 168n$$

Subtract $168n$ from both sides:

$$180n - 168n - 360 = 0$$

$$12n - 360 = 0$$

Add $360$ to both sides:

$$12n = 360$$

Divide both sides by $12$:

$$n = \frac{360}{12}$$

$$n = 30$$

Therefore, the number of sides of the polygon is

3

0.

3. Final Answer

A. 30