Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
(ii) 15 sides

Answer

To find the measure of each exterior angle of a regular polygon, we can use the formula:

\[ \text{Measure of each exterior angle} = \frac{360^\circ}{n} \]

where \( n \) is the number of sides of the polygon.

### Step-by-Step Solution

#### (i) For a polygon with 9 sides:

1. **Identify the number of sides (n)**: Here, \( n = 9 \).
2. **Use the formula**: Substitute \( n \) into the formula for the exterior angle.
\[ \text{Exterior angle} = \frac{360^\circ}{9} \]
3. **Calculate**:
\[ \text{Exterior angle} = 40^\circ \]

So, the measure of each exterior angle of a regular polygon with 9 sides is **40 degrees**.

#### (ii) For a polygon with 15 sides:

1. **Identify the number of sides (n)**: Here, \( n = 15 \).
2. **Use the formula**: Substitute \( n \) into the formula for the exterior angle.
\[ \text{Exterior angle} = \frac{360^\circ}{15} \]
3. **Calculate**:
\[ \text{Exterior angle} = 24^\circ \]

So, the measure of each exterior angle of a regular polygon with 15 sides is **24 degrees**.

### Final Answers:
- For a polygon with 9 sides: **40 degrees**
- For a polygon with 15 sides: **24 degrees**