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Central angle of a N sided Regular Polygon
  • Last Updated : 12 Apr, 2021

Given an integer N representing N sided regular polygon, the task is to find the angle made by the sides on the centre of the polygon that is the central angle.

The central angle is the angle formed by the two vertices forming an edge and the centre.

Examples: 

Input: N = 6 
Output: 60 
Explanation: 
The polygon is a hexagon with an angle 60 degree.

Input: N = 5 
Output: 72 
Explanation: 
The polygon is a pentagon with an angle 72 degree.



Approach: The idea is to observe that since there is a regular polygon all the central angles formed will be equal.
All central angles would add up to 360 degrees (a full circle), so the measure of the central angle is 360 divided by the number of sides.

Hence, central angle = 360 / N degrees, where N is the number of sides.

Below is the implementation of the above approach:

C++




// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate central
// angle of a polygon
double calculate_angle(double n)
{
    // Calculate the angle
    double total_angle = 360;
    return total_angle / n;
}
 
// Driver code
int main()
{
    double N = 5;
    cout << calculate_angle(N);
    return 0;
}

Java




// Java program for the above approach
class GFG{
 
// Function to calculate central
// angle of a polygon
static double calculate_angle(double n)
{
     
    // Calculate the angle
    double total_angle = 360;
    return total_angle / n;
}
 
// Driver code
public static void main(String[] args)
{
    double N = 5;
     
    System.out.println(calculate_angle(N));
}
}
 
// This code is contributed by rock_cool

Python3




# Python3 program for the above approach
 
# Function to calculate central
# angle of a polygon
def calculate_angle(n):
 
    # Calculate the angle
    total_angle = 360;
    return (total_angle // n)
 
# Driver code 
N = 5
 
print(calculate_angle(N))
 
# This code is contributed by rameshtravel07

Javascript




<script>
 
// Javascript program for the above approach
 
// Function to calculate central
// angle of a polygon
function calculate_angle(n)
{
     
    // Calculate the angle
    var total_angle = 360;
    return total_angle / n;
}
 
// Driver code
var N = 5;
   
document.write(calculate_angle(N));
 
// This code is contributed by Ankita saini
 
</script>
Output: 
72

Time Complexity: O(1) 
Auxiliary Space: O(1)
 

 

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