105 LearnersLast updated on June 25th, 2025
Interior Angles Of Polygon Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you're working on geometry projects, designing a home, or studying for exams, calculators make life easier. In this topic, we are going to talk about interior angles of polygon calculators.
What is Interior Angles Of Polygon Calculator?
An interior angles of polygon calculator is a tool to determine the sum of interior angles for a given polygon. Each polygon has a different number of sides, and this calculator helps to find the sum of its interior angles. This tool simplifies the process of calculating angles, saving time and effort.
How to Use the Interior Angles Of Polygon Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the number of sides: Input the number of sides of the polygon into the given field.
Step 2: Click on calculate: Click on the calculate button to get the result.
Step 3: View the result: The calculator will display the sum of the interior angles instantly.
How to Calculate Interior Angles of a Polygon?
To calculate the sum of interior angles of a polygon, there's a simple formula that the calculator uses:
Sum of interior angles = (n - 2) × 180°, where n is the number of sides in the polygon. This formula derives from dividing the polygon into triangles.
Each triangle has angles summing to 180°, and a polygon with n sides can be divided into (n - 2) triangles.
Tips and Tricks for Using the Interior Angles Of Polygon Calculator
When using an interior angles of polygon calculator, consider these tips to avoid mistakes:
Understand real-life applications like tiling or architectural designs. It helps in visualization.
Remember that the sum of angles increases with the number of sides.
Use the calculated angle sum to determine individual angles if the polygon is regular.
Common Mistakes and How to Avoid Them When Using the Interior Angles Of Polygon Calculator
While using a calculator, errors can occur. Here are some common mistakes to avoid:
Mistake 1
Miscounting the number of sides of the polygon.
Ensure the correct number of sides is entered. Incorrect inputs will lead to wrong results. For example, entering 5 sides for a hexagon will yield an incorrect sum of angles.
Mistake 2
Confusing internal angles with external angles.
The formula provided calculates interior angles. Do not use it to find exterior angles, which sum to 360° for any polygon.
Mistake 3
Incorrectly assuming the sum of angles for irregular polygons.
Even if a polygon is irregular, the formula for the sum of interior angles remains valid. Each set of sides creates the same number of triangles.
Mistake 4
Relying solely on the calculator for irregular polygons.
For irregular polygons, calculate individual angles separately. The calculator gives the sum, but you need additional steps for each angle.
Mistake 5
Assuming all calculators account for every polygonal nuance.
The calculator uses a basic formula. For complex polygons with additional constraints, manual verification may be necessary.
Interior Angles Of Polygon Calculator Examples
Problem 1
What is the sum of interior angles of a 12-sided polygon (dodecagon)?
Use the formula: Sum of interior angles = (n - 2) × 180°
Sum = (12 - 2) × 180° = 10 × 180° = 1800°
Explanation
A 12-sided polygon divides into 10 triangles, each contributing 180° to the sum of interior angles.
Problem 2
Calculate the sum of interior angles for a pentagon.
Use the formula: Sum of interior angles = (n - 2) × 180°
Sum = (5 - 2) × 180° = 3 × 180° = 540°
Explanation
A pentagon has 5 sides and can be divided into 3 triangles, resulting in a total sum of 540°.
Problem 3
How many degrees are the interior angles of an octagon?
Use the formula: Sum of interior angles = (n - 2) × 180°
Sum = (8 - 2) × 180° = 6 × 180° = 1080°
Explanation
An octagon can be split into 6 triangles, contributing a total of 1080° for the sum of its interior angles.
Problem 4
Find the sum of interior angles for a hexagon.
Use the formula: Sum of interior angles = (n - 2) × 180°
Sum = (6 - 2) × 180° = 4 × 180° = 720°
Explanation
A hexagon divides into 4 triangles, giving a sum of interior angles equal to 720°.
Problem 5
If a polygon has 15 sides, what is the sum of its interior angles?
Use the formula: Sum of interior angles = (n - 2) × 180°
Sum = (15 - 2) × 180° = 13 × 180° = 2340°
Explanation
A polygon with 15 sides can be divided into 13 triangles, resulting in an interior angle sum of 2340°.
FAQs on Using the Interior Angles Of Polygon Calculator
1.How do you calculate the sum of interior angles?
2.What is the sum of interior angles of a triangle?
3.Why do we subtract 2 from the number of sides?
4.How to use the interior angles of a polygon calculator?
5.Is the interior angles of polygon calculator accurate?
Glossary of Terms for the Interior Angles Of Polygon Calculator
- Interior Angles: The angles formed inside a polygon.
- Polygon: A closed figure with at least three straight sides.
- Regular Polygon: A polygon with all sides and angles equal.
- Sum of Interior Angles: The total of all interior angles in a polygon, calculated as (n - 2) × 180°.
- Irregular Polygon: A polygon with sides and angles not equal.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
