https://file.aiquickdraw.com/mathbot/file/1725366054011uubnuowa.jpg

The image you've uploaded seems to be a worksheet related to the measures of exterior angles and their respective sums for polygons. Here's a breakdown of the contents and how you can approach filling out the table and answering the questions:

### **Table: Measures of Exterior Angles and the Sides of Polygons**
- **First Column (Name of Polygon):** List the names of polygons (e.g., Triangle, Quadrilateral, Pentagon, etc.).
- **Second Column (Measure of One Exterior Angle):** Calculate or identify the measure of one exterior angle for each polygon.
- **Third Column (Number of Sides in the Polygon):** State the number of sides corresponding to the polygons listed.
- **Fourth Column (Sum of the Measures of the Exterior Angles):** The sum of the measures of the exterior angles for any polygon is always \(360^\circ\), regardless of the number of sides.

### **Questions:**
1. **What do you notice about the measure of the exterior angle of a regular polygon?**
   - Regular polygons have all exterior angles equal, and the measure of one exterior angle is \( \frac{360^\circ}{n} \), where \( n \) is the number of sides.

2. **What is common in the sums that you see in item 4?**
   - The sum of the exterior angles for any polygon is always \(360^\circ\), irrespective of the number of sides.

3. **Is the sum of exterior angles fixed or does it vary with the number of sides?**
   - The sum of the exterior angles is always fixed at \(360^\circ\).

4. **How do you find the sum of interior angles of a polygon?**
   - The sum of the interior angles of a polygon is given by the formula \( (n - 2) \times 180^\circ \), where \( n \) is the number of sides.

### **Next Steps:**
1. Fill out the table using the properties of polygons (regular and irregular).
2. Answer the provided questions based on the understanding of exterior angles.

### **Related Questions:**
1. What is the measure of one exterior angle in a regular hexagon?
2. How does the number of sides affect the measure of each exterior angle in a regular polygon?
3. If a polygon has 12 sides, what is the measure of one of its exterior angles?
4. Why is the sum of the exterior angles always \(360^\circ\) regardless of the polygon?
5. How would you find the measure of one interior angle in a regular octagon?

**Tip:** Remember, the sum of the exterior angles of a polygon is always constant at \(360^\circ\), which simplifies the calculations significantly!

Explore the measures of exterior angles and their sums for various polygons with this detailed worksheet. Understand how to calculate the exterior angle for each polygon and the constant sum of 360 degrees for the exterior angles. Ideal for high school students studying geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation