# Check if an N-sided Polygon is possible from N given angles

Last Updated : 13 Apr, 2021

Given an array arr[] of N elements, where each element represents an angle(in degrees) of a polygon, the task is to check whether it is possible to make an N-sided polygon with all the given angles or not. If it is possible then print Yes else print No.

Examples:

Input: N = 3, arr[] = {60, 60, 60}
Output: Yes
Explanation: There exists a triangle(i.e. a polygon) satisfying the above angles. Hence the output is Yes.

Input: N = 4, arr[] = {90, 90, 90, 100}
Output: No
Explanation: There does not exist any polygon satisfying the above angles. Hence the output is No.

Approach: A N-sided polygon is only possible if the sum of all the given angles is equal to 180*(N-2). Therefore the ides is to find the sum of all the angles given in the array arr[] and if the sum is equal to 180*(N-2) then print Yes, else print No.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach ` `#include ` `using` `namespace` `std; `   `// Function to check if the polygon ` `// exists or not ` `void` `checkValidPolygon(``int` `arr[], ``int` `N) ` `{ ` `    ``// Initialize a variable to ` `    ``// store the sum of angles ` `    ``int` `sum = 0; `   `    ``// Loop through the array and ` `    ``// calculate the sum of angles ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``sum += arr[i]; ` `    ``} `   `    ``// Check the condition for ` `    ``// an N-side polygon ` `    ``if` `(sum == 180 * (N - 2)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` `} `   `// Driver Code ` `int` `main() ` `{ ` `    ``int` `N = 3; `   `    ``// Given array arr[] ` `    ``int` `arr[] = { 60, 60, 60 }; `   `    ``// Function Call ` `    ``checkValidPolygon(arr, N); `   `    ``return` `0; ` `}`

## Java

 `// Java program for the above approach ` `import` `java.util.*; `   `class` `GFG{ ` `    `  `// Function to check if the polygon ` `// exists or not ` `static` `void` `checkValidPolygon(``int` `arr[], ``int` `N) ` `{ ` `    `  `    ``// Initialize a variable to ` `    ``// store the sum of angles ` `    ``int` `sum = ``0``; `   `    ``// Loop through the array and ` `    ``// calculate the sum of angles ` `    ``for``(``int` `i = ``0``; i < N; i++) ` `    ``{ ` `        ``sum += arr[i]; ` `    ``} `   `    ``// Check the condition for ` `    ``// an N-side polygon ` `    ``if` `(sum == ``180` `* (N - ``2``)) ` `        ``System.out.println(``"Yes"``); ` `    ``else` `        ``System.out.println(``"No"``); ` `} ` `    `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `N = ``3``; ` `    `  `    ``// Given array arr[] ` `    ``int` `arr[] = { ``60``, ``60``, ``60` `}; `   `    ``// Function call ` `    ``checkValidPolygon(arr, N); ` `} ` `} `   `// This code is contributed by offbeat `

## Python3

 `# Python3 program for the above approach`   `# Function to check if the polygon ` `# exists or not ` `def` `checkValidPolygon(arr, N): `   `    ``# Initialize a variable to ` `    ``# store the sum of angles ` `    ``Sum` `=` `0`   `    ``# Loop through the array and ` `    ``# calculate the sum of angles ` `    ``for` `i ``in` `range``(N): ` `        ``Sum` `+``=` `arr[i] `   `    ``# Check the condition for ` `    ``# an N-side polygon ` `    ``if` `Sum` `=``=` `180` `*` `(N ``-` `2``): ` `        ``print``(``"Yes"``)` `    ``else``:` `        ``print``(``"No"``)` `        `  `# Driver Code` `N ``=` `3`   `# Given array arr[] ` `arr ``=` `[ ``60``, ``60``, ``60` `] `   `# Function Call ` `checkValidPolygon(arr, N) `   `# This code is contributed by divyeshrabadiya07`

## C#

 `// C# program for the above approach` `using` `System;`   `class` `GFG{` `    `  `// Function to check if the polygon` `// exists or not` `static` `void` `checkValidPolygon(``int` `[]arr, ``int` `N)` `{` `    `  `    ``// Initialize a variable to` `    ``// store the sum of angles` `    ``int` `sum = 0;`   `    ``// Loop through the array and` `    ``// calculate the sum of angles` `    ``for``(``int` `i = 0; i < N; i++)` `    ``{` `        ``sum += arr[i];` `    ``}`   `    ``// Check the condition for` `    ``// an N-side polygon` `    ``if` `(sum == 180 * (N - 2))` `        ``Console.Write(``"Yes"``);` `    ``else` `        ``Console.Write(``"No"``);` `}` `    `  `// Driver code` `public` `static` `void` `Main(``string``[] args)` `{` `    ``int` `N = 3;` `    `  `    ``// Given array arr[]` `    ``int` `[]arr = { 60, 60, 60 };`   `    ``// Function call` `    ``checkValidPolygon(arr, N);` `}` `}`   `// This code is contributed by rutvik_56`

## Javascript

 ``

Output:

`Yes`

Time Complexity: O(N), where N is the length of the array.
Auxiliary Space: O(1)