Understanding Regular Polygons
A regular polygon is a geometric figure with all sides and angles equal. The interior angles of a polygon depend on the number of sides it has.
Formula for Interior Angles
The formula to find the measure of each interior angle of a regular polygon is:
- Interior Angle = (n - 2) * 180° / n
Where "n" is the number of sides of the polygon.
Minimum Interior Angle
To find the minimum interior angle, we need to consider polygons with the least number of sides:
- Triangle (3 sides):
- Interior Angle = (3 - 2) * 180° / 3 = 60°
- Quadrilateral (4 sides):
- Interior Angle = (4 - 2) * 180° / 4 = 90°
- Pentagon (5 sides):
- Interior Angle = (5 - 2) * 180° / 5 = 108°
As we increase the number of sides, the interior angle increases. Therefore, the polygon with the least number of sides, which is a triangle, has the smallest interior angle.
Conclusion
The minimum interior angle possible for a regular polygon is:
- 60° (Triangle)
This is the only regular polygon that maintains the smallest angle while still being a closed figure. Understanding these concepts is essential for grasping the fundamentals of geometry in Class 8.