Interior Angle of Regular Polygon Calculator

✖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.ⓘ Number of Sides of Regular Polygon [N_S]

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✖The Interior Angle of Regular Polygon is the angle between adjacent sides of a polygon.ⓘ Interior Angle of Regular Polygon [∠_Interior]

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Formula

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Interior Angle of Regular Polygon

Formula

`"∠"_{"Interior"} = (("N"_{"S"}-2)*pi)/"N"_{"S"}`

Example

`"135°"=(("8"-2)*pi)/"8"`

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Interior Angle of Regular Polygon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/Number of Sides of Regular Polygon
∠_Interior = ((N_S-2)*pi)/N_S
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Interior Angle of Regular Polygon - (Measured in Radian) - The Interior Angle of Regular Polygon is the angle between adjacent sides of a 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.

STEP 1: Convert Input(s) to Base Unit

Number of Sides of Regular Polygon: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Interior = ((N_S-2)*pi)/N_S --> ((8-2)*pi)/8

Evaluating ... ...

∠_Interior = 2.35619449019234

STEP 3: Convert Result to Output's Unit

2.35619449019234 Radian -->135.000000000025 Degree (Check conversion here)

FINAL ANSWER

135.000000000025 ≈ 135 Degree <-- Interior Angle of Regular Polygon

(Calculation completed in 00.004 seconds)

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Created by Sakshi Priya

Indian Institute of Technology (IIT), Roorkee

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< 4 Angles of Regular Polygon Calculators

Interior Angle of Regular Polygon

Go Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/Number of Sides of Regular Polygon

Interior Angle of Regular Polygon given Sum of Interior Angles

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

Sum of Interior Angles of Regular Polygon

Go Sum of Interior Angles of Regular Polygon = (Number of Sides of Regular Polygon-2)*pi

Exterior Angle of Regular Polygon

Go Exterior Angle of Regular Polygon = (2*pi)/Number of Sides of Regular Polygon

Interior Angle of Regular Polygon Formula

Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/Number of Sides of Regular Polygon
∠_Interior = ((N_S-2)*pi)/N_S

What is Regular Polygon?

A Regular polygon has sides of equal length and equal angles between each side. A regular n-sided polygon has rotational symmetry of order n and it is also known as a cyclic polygon. All the vertices of a regular polygon lie on the circumscribed circle.

What is Interior Angle?

The Interior angle of a polygon is the inner angle formed when two sides come together. All the interior angles in a regular polygon are equal.

How to Calculate Interior Angle of Regular Polygon?

Interior Angle of Regular Polygon calculator uses Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/Number of Sides of Regular Polygon to calculate 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 calculate Interior Angle of Regular Polygon using this online calculator? To use this online calculator for Interior Angle of Regular Polygon, enter Number of Sides of Regular Polygon (N_S) and hit the calculate button. Here is how the Interior Angle of Regular Polygon calculation can be explained with given input values -> 7734.93 = ((8-2)*pi)/8.

FAQ

What is Interior Angle of Regular Polygon?

Interior Angle of Regular Polygon formula can be defined as the angle between adjacent sides of a Polygon and is represented as ∠_Interior = ((N_S-2)*pi)/N_S or Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/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.

How to calculate Interior Angle of Regular Polygon?

Interior Angle of Regular Polygon formula can be defined as the angle between adjacent sides of a Polygon is calculated using Interior Angle of Regular Polygon = ((Number of Sides of Regular Polygon-2)*pi)/Number of Sides of Regular Polygon. To calculate Interior Angle of Regular Polygon, you need Number of Sides of Regular Polygon (N_S). With our tool, you need to enter the respective value for Number of Sides of Regular Polygon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Interior Angle of Regular Polygon?

In this formula, Interior Angle of Regular Polygon uses Number of Sides of Regular Polygon. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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