Sum of the Measures of the Exterior Angles of a Polygon
In this section, we explore the concept of exterior angles of polygons. An exterior angle is formed when you extend one side of the polygon. The section highlights that when you walk around a polygon and measure each turn you make (the exterior angle), the sum of these angles amounts to 360°. For instance, if you take a pentagon, as you walk along its edges and turn at each vertex, you will find that the cumulative measure of the turns is 360°. This relationship holds true for any polygon, regardless of the number of sides.
The section includes examples and problems prompting students to calculate unknown exterior angles using the established formula. Moreover, it emphasizes activities such as drawing polygons to physically demonstrate the concept and its universal applicability. This understanding lays the foundation for further exploration into polygon properties in geometry.
Similar Question: (Have to draw image manually by teacher)
Example : Find the number of sides of a regular polygon whose each exterior angle has a measure of 60°.
Solution: Total measure of all exterior angles = 360°
Measure of each exterior angle = 60°
Therefore, the number of exterior angles = \( \frac{360}{60} = 6 \).
The polygon has 6 sides.