32.) Each exterior angles of the regular n -gon has a measure of \( 3^{\circ} \)

To determine the number of sides \( n \) of a regular \( n \)-gon where each exterior angle measures \( 3^{\circ} \), you can use the following approach: ### **Understanding Exterior Angles of a Regular Polygon** 1. **Sum of Exterior Angles:** - For any polygon, the sum of all exterior angles is always \( 360^{\circ} \). 2. **Measure of Each Exterior Angle:** - In a **regular** polygon (where all sides and angles are equal), each exterior angle is given by: \[ \text{Each Exterior Angle} = \frac{360^{\circ}}{n} \] where \( n \) is the number of sides. ### **Given:** Each exterior angle is \( 3^{\circ} \). Therefore: \[ \frac{360^{\circ}}{n} = 3^{\circ} \] ### **Solving for \( n \):** \[ n = \frac{360^{\circ}}{3^{\circ}} = 120 \] ### **Conclusion:** The regular polygon has **120 sides**.