Inner Angle of Polygram given Outer Angle Calculator

✖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]			+10% -10%
✖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 given Outer Angle [∠_Inner]

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Formula

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Inner Angle of Polygram given Outer Angle

Formula

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

Example

`"74°"="110°"-(2*pi)/"10"`

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Inner Angle of Polygram given Outer Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Outer Angle of Polygram: 110 Degree --> 1.9198621771934 Radian (Check conversion here)
Number of Spikes in Polygram: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Inner = ∠_Outer-(2*pi)/N_Spikes --> 1.9198621771934-(2*pi)/10

Evaluating ... ...

∠_Inner = 1.29154364647544

STEP 3: Convert Result to Output's Unit

1.29154364647544 Radian -->73.9999999999932 Degree (Check conversion here)

FINAL ANSWER

73.9999999999932 ≈ 74 Degree <-- Inner Angle of Polygram

(Calculation completed in 00.004 seconds)

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Created by Jaseem K

IIT Madras (IIT Madras), Chennai

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< 2 Inner Angle of Polygram Calculators

Inner Angle of Polygram given Base Length

Go Inner Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Base Length of Polygram^2)/(2*Edge Length of Polygram^2))

Inner Angle of Polygram given Outer Angle

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

Inner Angle of Polygram given Outer Angle Formula

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

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 a n-pointed star. → For a 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 Inner Angle of Polygram given Outer Angle?

Inner Angle of Polygram given Outer Angle calculator uses Inner Angle of Polygram = Outer Angle of Polygram-(2*pi)/Number of Spikes in Polygram to calculate the Inner Angle of Polygram, The Inner Angle of Polygram given Outer Angle formula is defined as the unequal angle of the isosceles triangles attached to the Polygon of the Polygram and calculated using the outer angle. Inner Angle of Polygram is denoted by ∠_Inner symbol.

How to calculate Inner Angle of Polygram given Outer Angle using this online calculator? To use this online calculator for Inner Angle of Polygram given Outer Angle, enter Outer Angle of Polygram (∠_Outer) & Number of Spikes in Polygram (N_Spikes) and hit the calculate button. Here is how the Inner Angle of Polygram given Outer Angle calculation can be explained with given input values -> 4239.888 = 1.9198621771934-(2*pi)/10.

FAQ

What is Inner Angle of Polygram given Outer Angle?

The Inner Angle of Polygram given Outer Angle formula is defined as the unequal angle of the isosceles triangles attached to the Polygon of the Polygram and calculated using the outer angle and is represented as ∠_Inner = ∠_Outer-(2*pi)/N_Spikes or Inner Angle of Polygram = Outer Angle of Polygram-(2*pi)/Number of Spikes in Polygram. The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the 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.

How to calculate Inner Angle of Polygram given Outer Angle?

The Inner Angle of Polygram given Outer Angle formula is defined as the unequal angle of the isosceles triangles attached to the Polygon of the Polygram and calculated using the outer angle is calculated using Inner Angle of Polygram = Outer Angle of Polygram-(2*pi)/Number of Spikes in Polygram. To calculate Inner Angle of Polygram given Outer Angle, you need Outer Angle of Polygram (∠_Outer) & Number of Spikes in Polygram (N_Spikes). With our tool, you need to enter the respective value for Outer Angle of Polygram & Number of Spikes in 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 Inner Angle of Polygram?

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

Inner Angle of Polygram = arccos(((2*Edge Length of Polygram^2)-Base Length of Polygram^2)/(2*Edge Length of Polygram^2))

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