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Interior Angle of Regular Polygon Formula

GoInterior Angle of Regular Polygon given Sum of Interior Angles Formula

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The Interior Angle of Regular Polygon is the angle between adjacent sides of a polygon. Check FAQs

∠ Interior = \frac{(N S - 2) \cdot π}{N S}

∠_Interior - Interior Angle of Regular Polygon?N_S - Number of Sides of Regular Polygon?π - Archimedes' constant?

Interior Angle of Regular Polygon Example

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Here is how the Interior Angle of Regular Polygon equation looks like with Values.

Here is how the Interior Angle of Regular Polygon equation looks like with Units.

Here is how the Interior Angle of Regular Polygon equation looks like.

135 = \frac{(8 - 2) \cdot 3.1416}{8}

135° = \frac{(8 - 2) \cdot 3.1416}{8}

135 = \frac{(8 - 2) \cdot 3.1416}{8}

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Interior Angle of Regular Polygon Solution

Follow our step by step solution on how to calculate Interior Angle of Regular Polygon?

FIRST Step Consider the formula

∠ Interior = \frac{(N S - 2) \cdot π}{N S}

Next Step Substitute values of Variables

∴

∠ Interior = \frac{(8 - 2) \cdot π}{8}

Next Step Substitute values of Constants

∴

∠ Interior = \frac{(8 - 2) \cdot 3.1416}{8}

Next Step Prepare to Evaluate

∴

∠ Interior = \frac{(8 - 2) \cdot 3.1416}{8}

Next Step Evaluate

∴

∠ Interior = 2.35619449019234rad

Next Step Convert to Output's Unit

∴

∠ Interior = 135.000000000025°

LAST Step Rounding Answer

∴

∠ Interior = 135°

Interior Angle of Regular Polygon Formula Elements

Variables

Constants

Interior Angle of Regular Polygon

The Interior Angle of Regular Polygon is the angle between adjacent sides of a polygon.

Symbol: ∠_Interior

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Interior Angle of Regular Polygon

Number of Sides of Regular Polygon

The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons.

Symbol: N_S

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Sides of Regular Polygon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Interior Angle of Regular Polygon

Go Interior Angle of Regular Polygon given Sum of Interior Angles

∠ Interior = \frac{Sum∠ Interior}{N S}

Other formulas in Angles of Regular Polygon category

Go Exterior Angle of Regular Polygon

∠ Exterior = \frac{2 \cdot π}{N S}

Go Sum of Interior Angles of Regular Polygon

Sum∠ Interior = (N S - 2) \cdot π

How to Evaluate Interior Angle of Regular Polygon?

Interior Angle of Regular Polygon evaluator uses Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/Number of Sides of Regular Polygon to evaluate the Interior Angle of Regular Polygon, Interior Angle of Regular Polygon formula can be defined as the angle between adjacent sides of a Polygon. Interior Angle of Regular Polygon is denoted by ∠_Interior symbol.

How to evaluate Interior Angle of Regular Polygon using this online evaluator? To use this online evaluator for Interior Angle of Regular Polygon, enter Number of Sides of Regular Polygon (N_S) and hit the calculate button.

FAQs on Interior Angle of Regular Polygon

What is the formula to find Interior Angle of Regular Polygon?

The formula of Interior Angle of Regular Polygon is expressed as Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/Number of Sides of Regular Polygon. Here is an example- 7734.93 = ((8-2)*pi)/8.

How to calculate Interior Angle of Regular Polygon?

With Number of Sides of Regular Polygon (N_S) we can find Interior Angle of Regular Polygon using the formula - Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/Number of Sides of Regular Polygon. This formula also uses Archimedes' constant .

What are the other ways to Calculate Interior Angle of Regular Polygon?

Here are the different ways to Calculate Interior Angle of Regular Polygon-

Interior Angle of Regular Polygon=Sum of Interior Angles of Regular Polygon/Number of Sides of Regular Polygon

Can the Interior Angle of Regular Polygon be negative?

No, the Interior Angle of Regular Polygon, measured in Angle cannot be negative.

Which unit is used to measure Interior Angle of Regular Polygon?

Interior Angle of Regular Polygon is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Interior Angle of Regular Polygon can be measured.

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