Outer Angle of Polygram Calculator

✖The Number of Spikes in Polygram is the total count of isosceles triangular spikes the Polygram has or the total number of sides of the polygon on which the spikes are attached to form the Polygram.ⓘ Number of Spikes in Polygram [N_Spikes]			+10% -10%
✖The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.ⓘ Inner Angle of Polygram [∠_Inner]			+10% -10%

✖The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.ⓘ Outer Angle of Polygram [∠_Outer]

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Formula

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Outer Angle of Polygram

Formula

`"∠"_{"Outer"} = (2*pi)/"N"_{"Spikes"}+"∠"_{"Inner"}`

Example

`"110°" =(2*pi)/"10"+"74°"`

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Outer Angle of Polygram Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outer Angle of Polygram = (2*pi)/Number of Spikes in Polygram+Inner Angle of Polygram
∠_Outer = (2*pi)/N_Spikes+∠_Inner
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Outer Angle of Polygram - (Measured in Radian) - The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.
Number of Spikes in Polygram - The Number of Spikes in Polygram is the total count of isosceles triangular spikes the Polygram has or the total number of sides of the polygon on which the spikes are attached to form the Polygram.
Inner Angle of Polygram - (Measured in Radian) - The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.

STEP 1: Convert Input(s) to Base Unit

Number of Spikes in Polygram: 10 --> No Conversion Required
Inner Angle of Polygram: 74 Degree --> 1.29154364647556 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Outer = (2*pi)/N_Spikes+∠_Inner --> (2*pi)/10+1.29154364647556

Evaluating ... ...

∠_Outer = 1.91986217719352

STEP 3: Convert Result to Output's Unit

1.91986217719352 Radian -->110.000000000007 Degree (Check conversion here)

FINAL ANSWER

110.000000000007 ≈ 110 Degree <-- Outer Angle of Polygram

(Calculation completed in 00.004 seconds)

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< 2 Outer Angle of Polygram Calculators

Outer Angle of Polygram given Chord Length

Go Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2))

Outer Angle of Polygram

Go Outer Angle of Polygram = (2*pi)/Number of Spikes in Polygram+Inner Angle of Polygram

Outer Angle of Polygram Formula

Outer Angle of Polygram = (2*pi)/Number of Spikes in Polygram+Inner Angle of Polygram
∠_Outer = (2*pi)/N_Spikes+∠_Inner

What is Polygram ?

A Polygram is a regular n-sided polygon with identical isosceles triangles (also known as SPIKES) attached to each edge. It looks like an n-pointed star. For an n-pointed star, there will be n-spikes. The Spike (Isosceles Triangle) is an important part of the polygram and it is defined using 4 parameters. They are :
1) The Base Length of the Triangle (a.k.a Base Length of the Polygram)
2) Length of the equal side of the triangle (a.k.a Edge Length of the Polygram)
3) Angle between the two equal sides of the isosceles triangle (a.k.a Inner Angle angle of the Polygram)
4) Height of the triangle (a.k.a Spike Height)

Apart from these there are other important parameters that define the Polygram. They are:
1) Outer Angle : The angle between two adjacent isosceles triangles.
2) Chord Length : The distance between two peaks of the adjacent Spikes of the Polygram.
3) Perimeter : The sum of lengths of all the edges of the polygram.
4) Area : The amount of space occupied by the polygram.

How to Calculate Outer Angle of Polygram?

Outer Angle of Polygram calculator uses Outer Angle of Polygram = (2*pi)/Number of Spikes in Polygram+Inner Angle of Polygram to calculate the Outer Angle of Polygram, The Outer Angle of Polygram formula is defined as the angle between two adjacent isosceles triangles attached to the n-sided polygon of the whole Polygram. Outer Angle of Polygram is denoted by ∠_Outer symbol.

How to calculate Outer Angle of Polygram using this online calculator? To use this online calculator for Outer Angle of Polygram, enter Number of Spikes in Polygram (N_Spikes) & Inner Angle of Polygram (∠_Inner) and hit the calculate button. Here is how the Outer Angle of Polygram calculation can be explained with given input values -> 6302.536 = (2*pi)/10+1.29154364647556.

FAQ

What is Outer Angle of Polygram?

The Outer Angle of Polygram formula is defined as the angle between two adjacent isosceles triangles attached to the n-sided polygon of the whole Polygram and is represented as ∠_Outer = (2*pi)/N_Spikes+∠_Inner or Outer Angle of Polygram = (2*pi)/Number of Spikes in Polygram+Inner Angle of Polygram. The Number of Spikes in Polygram is the total count of isosceles triangular spikes the Polygram has or the total number of sides of the polygon on which the spikes are attached to form the Polygram & The Inner Angle of Polygram is the unequal angle of the isosceles triangle which forms the spikes of the Polygram or the angle inside the tip of any spike of Polygram.

How to calculate Outer Angle of Polygram?

The Outer Angle of Polygram formula is defined as the angle between two adjacent isosceles triangles attached to the n-sided polygon of the whole Polygram is calculated using Outer Angle of Polygram = (2*pi)/Number of Spikes in Polygram+Inner Angle of Polygram. To calculate Outer Angle of Polygram, you need Number of Spikes in Polygram (N_Spikes) & Inner Angle of Polygram (∠_Inner). With our tool, you need to enter the respective value for Number of Spikes in Polygram & Inner Angle of Polygram 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 Outer Angle of Polygram?

In this formula, Outer Angle of Polygram uses Number of Spikes in Polygram & Inner Angle of Polygram. We can use 1 other way(s) to calculate the same, which is/are as follows -

Outer Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Chord Length of Polygram^2)/(2*Edge Length of Polygram^2))

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