How do you calculate the interior angles of a polygon?

The sum of the interior angles of a polygon is calculated using the formula (n-2) × 180°, where n is the number of sides.

Polygon Interior Angles Calculator

This calculator helps you find the sum of interior angles of a polygon. Ideal for students, educators, and professionals working in geometry.

Calculator

Number of Sides *

Results

Sum of Interior Angles: 0°

Each Interior Angle: 0°

Data Source and Methodology

All calculations are strictly based on the formula for the sum of the interior angles of a polygon: (n-2) × 180°, where n is the number of sides.

The Formula Explained

The sum of the interior angles of a polygon is given by the formula:

Sum = (n - 2) * 180°

Glossary of Variables

n: Number of sides in the polygon.
Sum of Interior Angles: The total measure of all interior angles in the polygon.
Each Interior Angle: Average measure of each interior angle if the polygon is regular.

Frequently Asked Questions (FAQ)

What is a polygon?

A polygon is a 2D shape with straight sides. Examples include triangles, squares, and hexagons.

How do you find the interior angle of a regular polygon?

The measure of each interior angle in a regular polygon is given by the formula: (n - 2) × 180° / n.

What is the sum of interior angles of a triangle?

The sum of the interior angles of a triangle is always 180°.

Can a polygon have curved sides?

No, by definition, a polygon must have straight sides.

How many sides does a polygon need to have to be considered a polygon?

A polygon must have at least three sides.

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Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

, ', svg: { fontCache: 'global' } };

Polygon Interior Angles Calculator

This calculator helps you find the sum of interior angles of a polygon. Ideal for students, educators, and professionals working in geometry.

Calculator

Number of Sides *

Results

Sum of Interior Angles: 0°

Each Interior Angle: 0°

Data Source and Methodology

All calculations are strictly based on the formula for the sum of the interior angles of a polygon: (n-2) × 180°, where n is the number of sides.

The Formula Explained

The sum of the interior angles of a polygon is given by the formula:

Sum = (n - 2) * 180°

Glossary of Variables

n: Number of sides in the polygon.
Sum of Interior Angles: The total measure of all interior angles in the polygon.
Each Interior Angle: Average measure of each interior angle if the polygon is regular.

Frequently Asked Questions (FAQ)

What is a polygon?

A polygon is a 2D shape with straight sides. Examples include triangles, squares, and hexagons.

How do you find the interior angle of a regular polygon?

The measure of each interior angle in a regular polygon is given by the formula: (n - 2) × 180° / n.

What is the sum of interior angles of a triangle?

The sum of the interior angles of a triangle is always 180°.

Can a polygon have curved sides?

No, by definition, a polygon must have straight sides.

How many sides does a polygon need to have to be considered a polygon?

A polygon must have at least three sides.

```

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

]], displayMath: [['\\[','\\]']] }, svg: { fontCache: 'global' } };, svg: { fontCache: 'global' } };

Polygon Interior Angles Calculator

This calculator helps you find the sum of interior angles of a polygon. Ideal for students, educators, and professionals working in geometry.

Calculator

Number of Sides *

Results

Sum of Interior Angles: 0°

Each Interior Angle: 0°

Data Source and Methodology

All calculations are strictly based on the formula for the sum of the interior angles of a polygon: (n-2) × 180°, where n is the number of sides.

The Formula Explained

The sum of the interior angles of a polygon is given by the formula:

Sum = (n - 2) * 180°

Glossary of Variables

n: Number of sides in the polygon.
Sum of Interior Angles: The total measure of all interior angles in the polygon.
Each Interior Angle: Average measure of each interior angle if the polygon is regular.

Frequently Asked Questions (FAQ)

What is a polygon?

A polygon is a 2D shape with straight sides. Examples include triangles, squares, and hexagons.

How do you find the interior angle of a regular polygon?

The measure of each interior angle in a regular polygon is given by the formula: (n - 2) × 180° / n.

What is the sum of interior angles of a triangle?

The sum of the interior angles of a triangle is always 180°.

Can a polygon have curved sides?

No, by definition, a polygon must have straight sides.

How many sides does a polygon need to have to be considered a polygon?

A polygon must have at least three sides.

```

Audit: Complete

Formula (LaTeX) + variables + units

This section shows the formulas used by the calculator engine, plus variable definitions and units.

Formula (extracted LaTeX)

\[','\]

','

Variables and units

No variables provided in audit spec.

Sources (authoritative):

NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures
FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/

Changelog

Version: 0.1.0-draft
Last code update: 2026-01-19

0.1.0-draft · 2026-01-19

Initial audit spec draft generated from HTML extraction (review required).
Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
Confirm sources are authoritative and relevant to the calculator methodology.

Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn