The side length of a regular polygon doesn't directly determine its angles. The angles of a regular polygon are determined by the number of sides it has. Let's denote the number of sides as 'n' (instead of 'x' to avoid confusion with a variable representing length).
Here's how to determine the angles of a regular polygon:
1. Sum of Interior Angles:
The sum of the interior angles of any polygon (regular or irregular) is given by the formula:
Sum of interior angles = (n - 2) × 180°
Where 'n' is the number of sides.
2. Measure of Each Interior Angle (for a regular polygon):
In a regular polygon, all interior angles are equal. So, to find the measure of one interior angle, you divide the sum of the interior angles by the number of sides.
Each interior angle = [(n - 2) × 180°] / n
Alternatively, you can use the formula: Each interior angle = (180n - 360) / n.
3. Measure of Each Exterior Angle (for a regular polygon):
The sum of all exterior angles of any convex polygon is always 360°.
Since all exterior angles in a regular polygon are equal, you can find the measure of one exterior angle by dividing 360° by the number of sides.
Each exterior angle = 360° / n
4. Relationship between Interior and Exterior Angles:
At any vertex of a polygon, the interior angle and its corresponding exterior angle form a linear pair, meaning they add up to 180°.
Each interior angle = 180° - Each exterior angle.