Check if it is possible to create a polygon with a given angle in Python

Suppose we have an angle a. We need to check whether we can create a regular polygon where all interior angles are equal to a.

For example, if the input angle is 120°, the output will be True because a hexagon has all interior angles equal to 120°.

Mathematical Formula

The interior angle of a regular polygon is calculated using the formula ?

If n is a positive integer greater than 2, then we can form a regular polygon with the given angle.

Algorithm

To solve this problem, we follow these steps ?

• Calculate sides = 360 / (180 - a)
• Check if sides is a positive integer and greater than 2
• Return True if valid, False otherwise

Example

Let us see the implementation to get better understanding ?

def solve(a):
    sides = 360 / (180 - a)
    if sides == int(sides) and sides > 2:
        return True
    return False

# Test with angle 120 degrees
a = 120
result = solve(a)
print(f"Can create polygon with {a}° angles: {result}")

# Test with more examples
test_angles = [60, 90, 108, 135, 150]
for angle in test_angles:
    result = solve(angle)
    if result:
        n = int(360 / (180 - angle))
        print(f"{angle}° - Yes (forms {n}-sided polygon)")
    else:
        print(f"{angle}° - No")

Can create polygon with 120° angles: True
60° - Yes (forms 3-sided polygon)
90° - Yes (forms 4-sided polygon)
108° - Yes (forms 5-sided polygon)
135° - Yes (forms 8-sided polygon)
150° - Yes (forms 12-sided polygon)

How It Works

The formula n = 360 / (180 - a) comes from rearranging the interior angle formula. For a valid polygon ?

• The result must be a positive integer
• Must be greater than 2 (minimum 3 sides for a polygon)
• The angle must be less than 180° (interior angle constraint)

Edge Cases

def solve_with_validation(a):
    if a <= 0 or a >= 180:
        return False
    
    sides = 360 / (180 - a)
    return sides == int(sides) and sides > 2

# Test edge cases
test_cases = [0, 180, 179, 1, 60, 100]
for angle in test_cases:
    result = solve_with_validation(angle)
    print(f"Angle {angle}°: {result}")

Angle 0°: False
Angle 180°: False
Angle 179°: False
Angle 1°: False
Angle 60°: True
Angle 100°: False

Conclusion

Use the formula n = 360 / (180 - a) to check if a regular polygon can be formed with a given interior angle. The result must be a positive integer greater than 2 for a valid polygon.