Find the measure of each interior angle of a regular polygon of 15 sides:

Question

Accepted Answer

To find the measure of each interior angle of a regular polygon with 15 sides, we can use the formula for the interior angle of a regular polygon:

$$
\text{Interior Angle} = \frac{(n - 2) \times 180°}{n}
$$

where $ n $ is the number of sides of the polygon. For a polygon with 15 sides:

$$
\text{Interior Angle} = \frac{(15 - 2) \times 180°}{15} = \frac{13 \times 180°}{15} = \frac{2340°}{15} = 156°
$$

Therefore, the measure of each interior angle of a regular polygon with 15 sides is 156°, which corresponds to Option 2.

**Explanation for why Option 2 is correct:**

- The calculation above shows that using the formula for the interior angle of a regular polygon, we arrive at 156° for a polygon with 15 sides. This matches Option 2, confirming it as the correct answer.

**Explanation for why the other options are incorrect:**

1. **Option 1: 106°**
   - This value is incorrect because it is significantly lower than the calculated 156°. A regular polygon with 15 sides has angles much larger than 106°.

2. **Option 3: 206°**
   - This value is incorrect because it exceeds the calculated 156°. The interior angles of a regular polygon with 15 sides cannot be as large as 206°.

3. **Option 4: 256°**
   - This value is incorrect because it is far greater than the calculated 156°. Such a large angle is not possible for a regular polygon with 15 sides.

In conclusion, the correct measure of each interior angle of a regular polygon with 15 sides is 156°, making Option 2 the correct choice.