Understanding Exterior Angles of a Polygon
To solve the problem of finding the number of sides in a regular polygon with each exterior angle measuring 450 degrees, we first need to understand the properties of exterior angles in polygons.
Exterior Angle Formula
- The sum of all exterior angles of any polygon is always 360 degrees.
- For a regular polygon, each exterior angle can be calculated using the formula:
Exterior Angle = 360 degrees / Number of Sides (n)
Setting Up the Equation
Since we are given that each exterior angle measures 450 degrees, we can set up the equation:
- 450 = 360 / n
Solving for n
To find the number of sides (n), we rearrange the equation:
- n = 360 / 450
When we simplify this, we find:
- n = 0.8
However, this value does not make sense in the context of polygons, as the number of sides must be a whole number.
Correct Interpretation
The problem may contain a typographical error or misunderstanding. If we adjust the exterior angle to the correct measure of 45 degrees instead of 450 degrees, we can recalculate:
- 45 = 360 / n
- n = 360 / 45
- n = 8
Conclusion
Thus, the number of sides of a regular polygon whose each exterior angle measures 45 degrees is 8. Therefore, the correct answer is 'D'.
This highlights the importance of carefully interpreting angle measures in geometry to arrive at valid conclusions.