In the previous article, we have discussed about Java Program to Find Angle Subtended by the Chord to Center of the Circle If the Angle Subtended by Another Equal Chord of a Congruent Circle is Given

In this article we are going to see how to find Nth angle of a polygon whose initial angle and per angle increment is given by using Java programming language.

## Java Program to Find Nth Angle of a Polygon whose Initial Angle and Per Angle Increment is Given

Before Jumping into the program directly let’s see how to find Nth angle of a Polygon whose initial angle and per angle increment is given

Let the number of sides of the polygon is `N`

Initial angle of the polygon is `O`

Let the per angle increase be `P`

nth angle be `n`

i.e there is a N sides polygon with initial angle `O`

and difference `P`

nth angle = O + (n-1) * P

Using arithmetic Progression

Total nth angle = (n*((2*O)+(n-1)*P)/2

Now, we know the sum of N sided polygon (say S) = `180 * (N-2)`

Now, if (nth == S) then it is possible

Else not possible

**Example:**

N = 3 O = 30 P = 30 n = 3 Sum of nth angle = (n*((2*O)+(n-1)*P)/2 = 180 Sum of angle of N-sides polygon = 180*(N-2) = 180 nth angle = O + (n-1) * P = 90

Let’s see different ways to find Nth angle of a polygon whose initial angle and per angle increment is given.

### Method-1: Java Program to Find Nth Angle of a Polygon whose Initial Angle and Per Angle Increment is Given By Using Static Input Value

**Approach:**

- Declare an int variable say ‘
`N`

’ and assign the value to it, which holds the no of sides of the polygon. - Declare an double variable say ‘
`O`

’ and assign the value to it, which holds the initial angle of the polygon. - Declare an double variable say ‘
`P`

’ and assign the value to it, which holds the difference between 2 angle. - Declare an int variable say ‘
`n`

’ and assign the value to it, which holds the nth angle of the polygon - Find the Total nth angle using the formula
`(n*((2*O)+(n-1)*P)/2`

- Then find the sum of total angle of Nth side using the formula
`180*(N-2)`

- Now, check if
`total nth angle <= sum of angle of N sided polygon`

then print the result else print “Not Possible”.

**Program:**

import java.io.*; class Main { public static void main(String [] args) { int N = 3; double O = 30; double P = 30; int n = 2; // formula to find nth angle double nthAngle = O + (n-1) * P; // formula to find sum of nth angle double sumOfnthAngle = n*((2*O)+(n-1)*P)/2; // formula to find sum of angle of N-sides double sumOfAngleOfNside = 180*(N-2); // checking condition if (sumOfnthAngle <= sumOfAngleOfNside ) System.out.println("The nth angle is " + nthAngle); else System.out.println("Not Possible"); } }

Output: The nth angle is 60.0

### Method-2: Java Program to Find Nth Angle of a Polygon whose Initial Angle and Per Angle Increment is Given By Using User Input Value

**Approach:**

- Declare an int variable say ‘
`N`

’ and take the value as user input, which holds the no of sides of the polygon. - Declare an double variable say ‘
`O`

’ and take the value as user input, which holds the initial angle of the polygon. - Declare an double variable say ‘
`P`

’ and take the value as user input, which holds the difference between 2 angle. - Declare an int variable say ‘
`n`

’ and take the value as user input, which holds the nth angle of the polygon - Find the Total nth angle using the formula
`(n*((2*O)+(n-1)*P)/2`

- Then find the sum of total angle of Nth side using the formula
`180*(N-2)`

- Now, check if
`total nth angle <= sum of angle of N sided polygon`

then print the result else print “Not Possible”.

**Program:**

import java.io.*; import java.util.Scanner; class Main { public static void main(String [] args) { // scanner class obj ref Scanner s = new Scanner(System.in); System.out.print("Enter the no. Of sides of the polygon "); // to take user input value int N = s.nextInt(); System.out.print("Enter the initial angle of the polygon "); // to take user input value double O = s.nextDouble(); System.out.print("Enter the difference between 2 angle "); // to take user input value double P = s.nextDouble(); System.out.print("Enter n to find its nth angle "); // to take user input value int n = s.nextInt(); // formula to find nth angle double nthAngle = O + (n-1) * P; // formula to find sum of nth angle double sumOfnthAngle = n*((2*O)+(n-1)*P)/2; // formula to find sum of angle of N-sides double sumOfAngleOfNside = 180*(N-2); // checking condition if (sumOfnthAngle <= sumOfAngleOfNside ) System.out.println("The nth angle is " + nthAngle); else System.out.println("Not Possible"); } }

Output-1: Enter the no. Of sides of the polygon 3 Enter the initial angle of the polygon 30 Enter the difference between 2 angle 10 Enter n to find its nth angle 2 The nth angle is 40.0 Output-2: Enter the no. Of sides of the polygon 3 Enter the initial angle of the polygon 60 Enter the difference between 2 angle 10 Enter n to find its nth angle 3 Not Possible

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