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

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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