Outer angle of Polygram Calculator

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2D Geometry	Polygram ↺

✖Number of Points gives the number of corner points in the geometrical shape.ⓘ Number of Points [N_points]			+10% -10%
✖Inner angle is the interior angle of any geometric figure.ⓘ Inner angle [Angle_Inner]			+10% -10%

✖Outer angle is the angle between any side of the shape and a line extended from the next side.ⓘ Outer angle of Polygram [Angle_Outer]

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Credits

Jaseem K

IIT Madras (IIT Madras), Chennai

Jaseem K has created this Calculator and 100+ more calculators!

Nayana Phulphagar

Institute of chartered and financial Analysts of India National college (ICFAI National college), HUBLI

Nayana Phulphagar has verified this Calculator and 25+ more calculators!

Outer angle of Polygram Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outer angle = (2*pi/Number of Points)+Inner angle
Angle_Outer = (2*pi/N_points)+Angle_Inner
This formula uses 1 Constants, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Number of Points- Number of Points gives the number of corner points in the geometrical shape.
Inner angle - Inner angle is the interior angle of any geometric figure. (Measured in Degree)

STEP 1: Convert Input(s) to Base Unit

Number of Points: 5 --> No Conversion Required
Inner angle: 270 Degree --> 4.7123889803838 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Angle_Outer = (2*pi/N_points)+Angle_Inner --> (2*pi/5)+4.7123889803838

Evaluating ... ...

Angle_Outer = 5.96902604181972

STEP 3: Convert Result to Output's Unit

5.96902604181972 Radian -->342.000000000013 Degree (Check conversion here)

FINAL ANSWER

342.000000000013 Degree <-- Outer angle

(Calculation completed in 00.000 seconds)

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< 4 Polygram Calculators

Inner angle of Polygram

Inner angle = arccos((2*Length of edge^2-Base Length^2)/(2*Length of edge^2)) Go

Chord length of Polygram

Chord Length = sqrt(2*(Length of edge^2)*(1-cos(Outer angle))) Go

Outer angle of Polygram

Outer angle = (2*pi/Number of Points)+Inner angle Go

Perimeter of Polygram

Perimeter = 2*Number of Points*Length of edge Go

Outer angle of Polygram Formula

Outer angle = (2*pi/Number of Points)+Inner angle
Angle_Outer = (2*pi/N_points)+Angle_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 = (2*pi/Number of Points)+Inner angle to calculate the Outer angle, 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 is denoted by Angle_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 Points (N_points) & Inner angle (Angle_Inner) and hit the calculate button. Here is how the Outer angle of Polygram calculation can be explained with given input values -> 342 = (2*pi/5)+4.7123889803838.

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 Angle_Outer = (2*pi/N_points)+Angle_Inner or Outer angle = (2*pi/Number of Points)+Inner angle. Number of Points gives the number of corner points in the geometrical shape & Inner angle is the interior angle of any geometric figure.

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 = (2*pi/Number of Points)+Inner angle. To calculate Outer angle of Polygram, you need Number of Points (N_points) & Inner angle (Angle_Inner). With our tool, you need to enter the respective value for Number of Points & Inner angle 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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