MATH CALCULATOR
Polygon Angle Calculator
Calculate the interior and exterior angles of any polygon with ease.
What is the Polygon Angle Calculator & How does it work?
A polygon is a closed shape with straight sides. The sum of the interior angles of a polygon can be calculated using the formula:
(n – 2) Ο
n = number of sides
The measure of each interior angle in a regular polygon (where all angles are equal) is given by:
frac{(n – 2) Ο}{n}
n = number of sides
The exterior angle is supplementary to the interior angle, meaning their sum is always 180 degrees. For a regular polygon, each exterior angle can be calculated as:
frac{360}{n}
n = number of sides
Parameters
Resultβ
Frequently Asked Questions
How do I calculate the sum of interior angles in a polygon?
The sum of the interior angles of a polygon is calculated using the formula (n - 2) Γ 180 degrees, where n is the number of sides.
What is the measure of each interior angle in a regular polygon?
Each interior angle in a regular polygon can be found by dividing the sum of the interior angles by the number of sides: (n - 2) Γ 180 / n.
How do I find the measure of an exterior angle in a regular polygon?
The measure of each exterior angle in a regular polygon is calculated as 360 degrees divided by the number of sides: 360 / n.
Can this calculator help me with irregular polygons?
This calculator is specifically for regular polygons where all angles are equal. For irregular polygons, you would need to calculate each angle individually.
What is the relationship between interior and exterior angles in a polygon?
The interior and exterior angles of a polygon are supplementary, meaning they add up to 180 degrees at each vertex.
How many sides does a regular polygon have if each interior angle measures 150 degrees?
To find the number of sides, use the formula: n = 360 / (180 - interior angle). For a 150-degree angle, n = 360 / (180 - 150) = 12 sides.
Is there a limit to the number of sides this calculator can handle?
No, this calculator can handle polygons with any number of sides, as long as it is a positive integer greater than or equal to 3.
Results are for informational purposes only and do not constitute professional advice.