Find the Measure of Each Angle Calculator
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Find the Measure of Each Angle Calculator
Use this calculator to find the measure of each interior angle in a regular polygon when you know the number of sides.
Number of Sides (n):
Calculate Angle
Reset
Understanding Interior Angles of Polygons
A polygon is a closed shape made of straight line segments. The interior angles of a polygon are the angles inside the polygon at each vertex (corner).
For any convex polygon (a polygon where all interior angles are less than 180 degrees), the sum of the interior angles can be calculated using the formula:
Sum of Interior Angles = (n - 2) * 180 degrees
where 'n' represents the number of sides of the polygon.
Calculating Each Interior Angle of a Regular Polygon
A regular polygon is a polygon that is both equilateral (all sides are equal in length) and equiangular (all interior angles have the same measure).
To find the measure of each interior angle in a regular polygon, we divide the total sum of interior angles by the number of sides (or vertices, which is the same number 'n'):
Measure of Each Interior Angle = [(n - 2) * 180 degrees] / n
How the Calculator Works
This calculator takes the number of sides (n) of a regular polygon as input. It then applies the formula:
It calculates the sum of all interior angles using (n - 2) * 180.
It divides this sum by the number of sides (n) to find the measure of a single interior angle.
Examples
Triangle (n=3):
Sum = (3 – 2) * 180 = 1 * 180 = 180 degrees
Each Angle = 180 / 3 = 60 degrees (an equilateral triangle)
Square (n=4):
Sum = (4 – 2) * 180 = 2 * 180 = 360 degrees
Each Angle = 360 / 4 = 90 degrees (a square has four right angles)
Pentagon (n=5):
Sum = (5 – 2) * 180 = 3 * 180 = 540 degrees
Each Angle = 540 / 5 = 108 degrees
Hexagon (n=6):
Sum = (6 – 2) * 180 = 4 * 180 = 720 degrees
Each Angle = 720 / 6 = 120 degrees
When is this Useful?
Geometry Students: Helps in understanding and verifying polygon properties.Tessellation Design: Useful for determining if shapes can tile a surface without gaps or overlaps.Architecture and Engineering: Basic geometric calculations for design and construction.Mathematics Education: A practical tool for learning about geometric shapes.
function calculateAngle() {
var sidesInput = document.getElementById("numberOfSides");
var resultDiv = document.getElementById("result");
var errorDiv = document.getElementById("errorMessage");
// Clear previous error messages
errorDiv.style.display = 'none';
errorDiv.textContent = ";
var n = parseFloat(sidesInput.value);
// Input validation
if (isNaN(n)) {
errorDiv.textContent = 'Please enter a valid number for the number of sides.';
errorDiv.style.display = 'block';
resultDiv.textContent = ";
return;
}
if (n < 3) {
errorDiv.textContent = 'A polygon must have at least 3 sides.';
errorDiv.style.display = 'block';
resultDiv.textContent = '';
return;
}
// Calculation
// Formula: [(n – 2) * 180] / n
var sumOfAngles = (n – 2) * 180;
var eachAngle = sumOfAngles / n;
// Display result
resultDiv.textContent = eachAngle.toFixed(2) + ' degrees';
}
function resetForm() {
document.getElementById("numberOfSides").value = '';
document.getElementById("result").textContent = '';
document.getElementById("errorMessage").style.display = 'none';
document.getElementById("errorMessage").textContent = '';
}