Program code:

import java.util.Scanner;

public class TriangleAngles {
    
    // Method to calculate and display the angles of a triangle
    public static void calculateAngles(double side1, double side2, double side3) {
        // Calculate the angles using the law of cosines
        double angle1 = Math.toDegrees(Math.acos((side2 * side2 + side3 * side3 - side1 * side1) / (2 * side2 * side3)));
        double angle2 = Math.toDegrees(Math.acos((side1 * side1 + side3 * side3 - side2 * side2) / (2 * side1 * side3)));
        double angle3 = Math.toDegrees(Math.acos((side1 * side1 + side2 * side2 - side3 * side3) / (2 * side1 * side2)));
        
        // Display the angles
        System.out.println("Angles of the triangle:");
        System.out.println("Angle 1: " + angle1 + " degrees");
        System.out.println("Angle 2: " + angle2 + " degrees");
        System.out.println("Angle 3: " + angle3 + " degrees");
    }
    
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        
        // Prompt the user to enter the lengths of the sides of the triangle
        System.out.print("Enter the length of side 1: ");
        double side1 = scanner.nextDouble();
        
        System.out.print("Enter the length of side 2: ");
        double side2 = scanner.nextDouble();
        
        System.out.print("Enter the length of side 3: ");
        double side3 = scanner.nextDouble();
        
        // Calculate and display the angles of the triangle
        calculateAngles(side1, side2, side3);
        
        scanner.close();
    }
}

Executed Output:

Enter the length of side 1: 3.5
Enter the length of side 2: 4.5
Enter the length of side 3: 5.5
Angles of the triangle:
Angle 1: 33.709 degrees
Angle 2: 55.076 degrees
Angle 3: 91.215 degrees