The measure of an exterior angle of a regular polygon is given below. Find the measure of an interior angle. Then find the number of sides. 40 What is the measure of an interior angle? 140 How many sides does the polygon have? ?

To solve the problem, let's break it down into two parts: 1. **Finding the Measure of an Interior Angle** 2. **Determining the Number of Sides of the Polygon** --- ### 1. Measure of an Interior Angle For any polygon, the **interior angle** and the **exterior angle** at each vertex are supplementary. This means they add up to 180 degrees. Given: - **Exterior Angle (E)** = 40° **Interior Angle (I)** = 180° - Exterior Angle **I** = 180° - 40° **I** = 140° **Answer:** The measure of an interior angle is **140 degrees**. --- ### 2. Number of Sides of the Polygon The sum of all exterior angles of any polygon is always 360 degrees. For a **regular polygon** (where all exterior angles are equal), the number of sides (**n**) can be found using the formula: \[ n = \frac{360°}{\text{Exterior Angle (E)}} \] Given: - **Exterior Angle (E)** = 40° \[ n = \frac{360°}{40°} = 9 \] **Answer:** The polygon has **9 sides**. --- ### Summary - **Interior Angle:** 140° - **Number of Sides:** 9 This polygon is a **nonagon** (a nine-sided polygon).