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Inner Angle of Polygram given Outer Angle Formula

GoInner Angle of Polygram given Base Length Formula

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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. Check FAQs

∠ Inner = ∠ Outer - \frac{2 \cdot π}{N Spikes}

∠_Inner - Inner Angle of Polygram?∠_Outer - Outer Angle of Polygram?N_Spikes - Number of Spikes in Polygram?π - Archimedes' constant?

Inner Angle of Polygram given Outer Angle Example

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Here is how the Inner Angle of Polygram given Outer Angle equation looks like with Values.

Here is how the Inner Angle of Polygram given Outer Angle equation looks like with Units.

Here is how the Inner Angle of Polygram given Outer Angle equation looks like.

74 = 110 - \frac{2 \cdot 3.1416}{10}

74° = 110° - \frac{2 \cdot 3.1416}{10}

74 = 110 - \frac{2 \cdot 3.1416}{10}

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Inner Angle of Polygram given Outer Angle Solution

Follow our step by step solution on how to calculate Inner Angle of Polygram given Outer Angle?

FIRST Step Consider the formula

∠ Inner = ∠ Outer - \frac{2 \cdot π}{N Spikes}

Next Step Substitute values of Variables

∴

∠ Inner = 110° - \frac{2 \cdot π}{10}

Next Step Substitute values of Constants

∴

∠ Inner = 110° - \frac{2 \cdot 3.1416}{10}

Next Step Convert Units

∴

∠ Inner = 1.9199rad - \frac{2 \cdot 3.1416}{10}

Next Step Prepare to Evaluate

∴

∠ Inner = 1.9199 - \frac{2 \cdot 3.1416}{10}

Next Step Evaluate

∴

∠ Inner = 1.29154364647544rad

Next Step Convert to Output's Unit

∴

∠ Inner = 73.9999999999932°

LAST Step Rounding Answer

∴

∠ Inner = 74°

Inner Angle of Polygram given Outer Angle Formula Elements

Variables

Constants

Inner Angle of 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.

Symbol: ∠_Inner

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Inner Angle of Polygram

Outer Angle of Polygram

The Outer Angle of Polygram is the angle between any two adjacent isosceles triangles which forms the spikes of the Polygram.

Symbol: ∠_Outer

Measurement: AngleUnit: °

Note: Value should be between 0 to 300.

Formulas to find Outer Angle of 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.

Symbol: N_Spikes

Measurement: NAUnit: Unitless

Note: Value should be greater than 2.

Formulas to find Number of Spikes in Polygram

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 Inner Angle of Polygram

Go Inner Angle of Polygram given Base Length

∠ Inner = \arccos (\frac{(2 \cdot {l e}^{2}) - {l Base}^{2}}{2 \cdot {l e}^{2}})

How to Evaluate Inner Angle of Polygram given Outer Angle?

Inner Angle of Polygram given Outer Angle evaluator uses Inner Angle of Polygram = Outer Angle of Polygram-(2*pi)/Number of Spikes in Polygram to evaluate 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 evaluate Inner Angle of Polygram given Outer Angle using this online evaluator? To use this online evaluator 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.

FAQs on Inner Angle of Polygram given Outer Angle

What is the formula to find Inner Angle of Polygram given Outer Angle?

The formula of Inner Angle of Polygram given Outer Angle is expressed as Inner Angle of Polygram = Outer Angle of Polygram-(2*pi)/Number of Spikes in Polygram. Here is an example- 4239.888 = 1.9198621771934-(2*pi)/10.

How to calculate Inner Angle of Polygram given Outer Angle?

With Outer Angle of Polygram (∠_Outer) & Number of Spikes in Polygram (N_Spikes) we can find Inner Angle of Polygram given Outer Angle using the formula - Inner Angle of Polygram = Outer Angle of Polygram-(2*pi)/Number of Spikes in Polygram. This formula also uses Archimedes' constant .

What are the other ways to Calculate Inner Angle of Polygram?

Here are the different ways to Calculate Inner Angle of Polygram-

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

Can the Inner Angle of Polygram given Outer Angle be negative?

No, the Inner Angle of Polygram given Outer Angle, measured in Angle cannot be negative.

Which unit is used to measure Inner Angle of Polygram given Outer Angle?

Inner Angle of Polygram given Outer Angle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Inner Angle of Polygram given Outer Angle can be measured.

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