Find the measure of each exterior angle of a regular
(i) pentagon (ii) hexagon (iii) heptagon (iv) decagon (v) polygon of 15 sides.

Answer

To find the measure of each exterior angle of the given regular polygons, we can use the formula for the exterior angle of a regular polygon, which is:

\[ \text{Exterior Angle} = \frac{360^\circ}{n} \]

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

Now, let's calculate the exterior angles for each polygon step by step.

### (i) Pentagon
1. **Identify the number of sides**: A pentagon has \( n = 5 \) sides.
2. **Apply the formula**:
\[ \text{Exterior Angle} = \frac{360^\circ}{5} = 72^\circ \]

### (ii) Hexagon
1. **Identify the number of sides**: A hexagon has \( n = 6 \) sides.
2. **Apply the formula**:
\[ \text{Exterior Angle} = \frac{360^\circ}{6} = 60^\circ \]

### (iii) Heptagon
1. **Identify the number of sides**: A heptagon has \( n = 7 \) sides.
2. **Apply the formula**:
\[ \text{Exterior Angle} = \frac{360^\circ}{7} \approx 51.43^\circ \]

### (iv) Decagon
1. **Identify the number of sides**: A decagon has \( n = 10 \) sides.
2. **Apply the formula**:
\[ \text{Exterior Angle} = \frac{360^\circ}{10} = 36^\circ \]

### (v) Polygon of 15 sides
1. **Identify the number of sides**: This polygon has \( n = 15 \) sides.
2. **Apply the formula**:
\[ \text{Exterior Angle} = \frac{360^\circ}{15} = 24^\circ \]

### Summary of Results
- **Pentagon**: \( 72^\circ \)
- **Hexagon**: \( 60^\circ \)
- **Heptagon**: \( \approx 51.43^\circ \)
- **Decagon**: \( 36^\circ \)
- **15-sided polygon**: \( 24^\circ \)