Sum of Interior Angles of N-gon Calculator

✖Sum of Interior Angles of N-gon is the sum of all the interior angles of an N sided polygon.ⓘ Sum of Interior Angles of N-gon [Sum_{Interior Angles}]

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Formula

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Sum of Interior Angles of N-gon

Formula

`"Sum"_{"Interior Angles"} = ("N"_{"Sides"}-2)*pi`

Example

`"1080°"=("8"-2)*pi`

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Sum of Interior Angles of N-gon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Sum of Interior Angles of N-gon = (Number of Sides of N-gon-2)*pi
Sum_{Interior Angles} = (N_Sides-2)*pi
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Sum of Interior Angles of N-gon - (Measured in Radian) - Sum of Interior Angles of N-gon is the sum of all the interior angles of an N sided polygon.
Number of Sides of N-gon - Number of Sides of N-gon is the number of line segments required to make a N-gon.

STEP 1: Convert Input(s) to Base Unit

Number of Sides of N-gon: 8 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Sum_{Interior Angles} = (N_Sides-2)*pi --> (8-2)*pi

Evaluating ... ...

Sum_{Interior Angles} = 18.8495559215388

STEP 3: Convert Result to Output's Unit

18.8495559215388 Radian -->1080.0000000002 Degree (Check conversion here)

FINAL ANSWER

1080.0000000002 ≈ 1080 Degree <-- Sum of Interior Angles of N-gon

(Calculation completed in 00.004 seconds)

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Created by Anamika Mittal

Vellore Institute of Technology (VIT), Bhopal

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Verified by Mona Gladys

St Joseph's College (SJC), Bengaluru

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< 4 Angles of N-gon Calculators

Sum of Exterior Angles of N-gon

Go Sum of Exterior Angles of N-gon = 2*pi*(Number of Sides of N-gon/Number of Sides of N-gon)

Sum of Interior Angles of N-gon

Go Sum of Interior Angles of N-gon = (Number of Sides of N-gon-2)*pi

Exterior Angle of N-gon

Go Exterior Angle of N-gon = (2*pi)/Number of Sides of N-gon

Central Angle of N-gon

Go Central Angle of N-gon = (2*pi)/Number of Sides of N-gon

Sum of Interior Angles of N-gon Formula

Sum of Interior Angles of N-gon = (Number of Sides of N-gon-2)*pi
Sum_{Interior Angles} = (N_Sides-2)*pi

What is N-gon?

N-gon is a polygon with N sides and N vertices. An n-gon, can be either convex or concave. A convex polygon has none of its interior angles greater than 180°. On the contrary, a concave polygon has one or more of its interior angles greater than 180°. A polygon is called regular when its sides are equal and also its interior angles are equal.

What is an Interior and an Exterior angle?

An interior angle of a polygon is the angle between two sides of a polygon while an exterior angle is formed by extending a side of a polygon.

How to Calculate Sum of Interior Angles of N-gon?

Sum of Interior Angles of N-gon calculator uses Sum of Interior Angles of N-gon = (Number of Sides of N-gon-2)*pi to calculate the Sum of Interior Angles of N-gon, Sum of Interior Angles of N-gon is defined as the addition of all the interior angles of the N-sided Polygon. Sum of Interior Angles of N-gon is denoted by Sum_{Interior Angles} symbol.

How to calculate Sum of Interior Angles of N-gon using this online calculator? To use this online calculator for Sum of Interior Angles of N-gon, enter Number of Sides of N-gon (N_Sides) and hit the calculate button. Here is how the Sum of Interior Angles of N-gon calculation can be explained with given input values -> 61879.44 = (8-2)*pi.

FAQ

What is Sum of Interior Angles of N-gon?

Sum of Interior Angles of N-gon is defined as the addition of all the interior angles of the N-sided Polygon and is represented as Sum_{Interior Angles} = (N_Sides-2)*pi or Sum of Interior Angles of N-gon = (Number of Sides of N-gon-2)*pi. Number of Sides of N-gon is the number of line segments required to make a N-gon.

How to calculate Sum of Interior Angles of N-gon?

Sum of Interior Angles of N-gon is defined as the addition of all the interior angles of the N-sided Polygon is calculated using Sum of Interior Angles of N-gon = (Number of Sides of N-gon-2)*pi. To calculate Sum of Interior Angles of N-gon, you need Number of Sides of N-gon (N_Sides). With our tool, you need to enter the respective value for Number of Sides of N-gon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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