Reflex Angle of Concave Quadrilateral Calculator

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✖The First Acute Angle of Concave Quadrilateral is the angle formed between the first outer and first inner side of the Concave Quadrilateral.ⓘ First Acute Angle of Concave Quadrilateral [∠_{First Acute}]			+10% -10%
✖Third Acute Angle of Concave Quadrilateral is the angle formed between both the outer sides of the Concave Quadrilateral.ⓘ Third Acute Angle of Concave Quadrilateral [∠_{Third Acute}]			+10% -10%
✖Second Acute Angle of Concave Quadrilateral is the angle formed between second outer and second inner side of the Concave Quadrilateral.ⓘ Second Acute Angle of Concave Quadrilateral [∠_{Second Acute}]			+10% -10%

✖The Reflex Angle of Concave Quadrilateral is the angle formed between both the inner sides of the figure which measures more than 180 degree and less than 360 degree.ⓘ Reflex Angle of Concave Quadrilateral [∠_Reflex]

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Formula

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Reflex Angle of Concave Quadrilateral

Formula

`"∠"_{"Reflex"} = (2*pi)-("∠"_{"First Acute"}+"∠"_{"Third Acute"}+"∠"_{"Second Acute"})`

Example

`"243°"=(2*pi)-("17°"+"55°"+"45°")`

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Reflex Angle of Concave Quadrilateral Solution

STEP 0: Pre-Calculation Summary

Formula Used

Reflex Angle of Concave Quadrilateral = (2*pi)-(First Acute Angle of Concave Quadrilateral+Third Acute Angle of Concave Quadrilateral+Second Acute Angle of Concave Quadrilateral)
∠_Reflex = (2*pi)-(∠_{First Acute}+∠_{Third Acute}+∠_{Second Acute})
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Reflex Angle of Concave Quadrilateral - (Measured in Radian) - The Reflex Angle of Concave Quadrilateral is the angle formed between both the inner sides of the figure which measures more than 180 degree and less than 360 degree.
First Acute Angle of Concave Quadrilateral - (Measured in Radian) - The First Acute Angle of Concave Quadrilateral is the angle formed between the first outer and first inner side of the Concave Quadrilateral.
Third Acute Angle of Concave Quadrilateral - (Measured in Radian) - Third Acute Angle of Concave Quadrilateral is the angle formed between both the outer sides of the Concave Quadrilateral.
Second Acute Angle of Concave Quadrilateral - (Measured in Radian) - Second Acute Angle of Concave Quadrilateral is the angle formed between second outer and second inner side of the Concave Quadrilateral.

STEP 1: Convert Input(s) to Base Unit

First Acute Angle of Concave Quadrilateral: 17 Degree --> 0.29670597283898 Radian (Check conversion here)
Third Acute Angle of Concave Quadrilateral: 55 Degree --> 0.959931088596701 Radian (Check conversion here)
Second Acute Angle of Concave Quadrilateral: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠_Reflex = (2*pi)-(∠_{First Acute}+∠_{Third Acute}+∠_{Second Acute}) --> (2*pi)-(0.29670597283898+0.959931088596701+0.785398163397301)

Evaluating ... ...

∠_Reflex = 4.2411500823466

STEP 3: Convert Result to Output's Unit

4.2411500823466 Radian -->243.000000000068 Degree (Check conversion here)

FINAL ANSWER

243.000000000068 ≈ 243 Degree <-- Reflex Angle of Concave Quadrilateral

(Calculation completed in 00.020 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Walchand College of Engineering (WCE), Sangli

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< 7 Concave Quadrilateral Calculators

Area of Concave Quadrilateral

Go Area of Concave Quadrilateral = sqrt(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Outer Side of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((First Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+First Inner Side of Concave Quadrilateral)/2)-First Inner Side of Concave Quadrilateral))+sqrt(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Outer Side of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Inner Diagonal of Concave Quadrilateral)*(((Second Outer Side of Concave Quadrilateral+Inner Diagonal of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral)/2)-Second Inner Side of Concave Quadrilateral))

Inner Diagonal of Concave Quadrilateral

Go Inner Diagonal of Concave Quadrilateral = sqrt(Second Outer Side of Concave Quadrilateral^2+Second Inner Side of Concave Quadrilateral^2-(2*Second Outer Side of Concave Quadrilateral*Second Inner Side of Concave Quadrilateral*cos(Third Acute Angle of Concave Quadrilateral)))

Outer Diagonal of Concave Quadrilateral

Go Outer Diagonal of Concave Quadrilateral = sqrt(First Outer Side of Concave Quadrilateral^2+Second Outer Side of Concave Quadrilateral^2-(2*First Outer Side of Concave Quadrilateral*Second Outer Side of Concave Quadrilateral*cos(Second Acute Angle of Concave Quadrilateral)))

First Inner Side of Concave Quadrilateral

Go First Inner Side of Concave Quadrilateral = sqrt(First Outer Side of Concave Quadrilateral^2+Outer Diagonal of Concave Quadrilateral^2-(2*First Outer Side of Concave Quadrilateral*Outer Diagonal of Concave Quadrilateral*cos(Second Acute Angle of Concave Quadrilateral)))

First Acute Angle of Concave Quadrilateral

Go First Acute Angle of Concave Quadrilateral = arccos((First Outer Side of Concave Quadrilateral^2+First Inner Side of Concave Quadrilateral^2-Inner Diagonal of Concave Quadrilateral^2)/(2*First Outer Side of Concave Quadrilateral*First Inner Side of Concave Quadrilateral))

Perimeter of Concave Quadrilateral

Go Perimeter of Concave Quadrilateral = First Outer Side of Concave Quadrilateral+Second Outer Side of Concave Quadrilateral+Second Inner Side of Concave Quadrilateral+First Inner Side of Concave Quadrilateral

Reflex Angle of Concave Quadrilateral

Go Reflex Angle of Concave Quadrilateral = (2*pi)-(First Acute Angle of Concave Quadrilateral+Third Acute Angle of Concave Quadrilateral+Second Acute Angle of Concave Quadrilateral)

Reflex Angle of Concave Quadrilateral Formula

What is a Concave Quadrilateral?

A Quadrilateral is called a concave quadrilateral, if at least one line segment joining the vertices is not a part of the same region of the quadrilateral. That is, any line segment that joins two interior points goes outside the figure.

How to Calculate Reflex Angle of Concave Quadrilateral?

Reflex Angle of Concave Quadrilateral calculator uses Reflex Angle of Concave Quadrilateral = (2*pi)-(First Acute Angle of Concave Quadrilateral+Third Acute Angle of Concave Quadrilateral+Second Acute Angle of Concave Quadrilateral) to calculate the Reflex Angle of Concave Quadrilateral, The Reflex angle of Concave Quadrilateral formula is defined as the angle which is formed by the intersection of both the inner sides of the Concave Quadrilateral. Reflex Angle of Concave Quadrilateral is denoted by ∠_Reflex symbol.

How to calculate Reflex Angle of Concave Quadrilateral using this online calculator? To use this online calculator for Reflex Angle of Concave Quadrilateral, enter First Acute Angle of Concave Quadrilateral (∠_{First Acute}), Third Acute Angle of Concave Quadrilateral (∠_{Third Acute}) & Second Acute Angle of Concave Quadrilateral (∠_{Second Acute}) and hit the calculate button. Here is how the Reflex Angle of Concave Quadrilateral calculation can be explained with given input values -> 13922.87 = (2*pi)-(0.29670597283898+0.959931088596701+0.785398163397301).

FAQ

What is Reflex Angle of Concave Quadrilateral?

The Reflex angle of Concave Quadrilateral formula is defined as the angle which is formed by the intersection of both the inner sides of the Concave Quadrilateral and is represented as ∠_Reflex = (2*pi)-(∠_{First Acute}+∠_{Third Acute}+∠_{Second Acute}) or Reflex Angle of Concave Quadrilateral = (2*pi)-(First Acute Angle of Concave Quadrilateral+Third Acute Angle of Concave Quadrilateral+Second Acute Angle of Concave Quadrilateral). The First Acute Angle of Concave Quadrilateral is the angle formed between the first outer and first inner side of the Concave Quadrilateral, Third Acute Angle of Concave Quadrilateral is the angle formed between both the outer sides of the Concave Quadrilateral & Second Acute Angle of Concave Quadrilateral is the angle formed between second outer and second inner side of the Concave Quadrilateral.

How to calculate Reflex Angle of Concave Quadrilateral?

The Reflex angle of Concave Quadrilateral formula is defined as the angle which is formed by the intersection of both the inner sides of the Concave Quadrilateral is calculated using Reflex Angle of Concave Quadrilateral = (2*pi)-(First Acute Angle of Concave Quadrilateral+Third Acute Angle of Concave Quadrilateral+Second Acute Angle of Concave Quadrilateral). To calculate Reflex Angle of Concave Quadrilateral, you need First Acute Angle of Concave Quadrilateral (∠_{First Acute}), Third Acute Angle of Concave Quadrilateral (∠_{Third Acute}) & Second Acute Angle of Concave Quadrilateral (∠_{Second Acute}). With our tool, you need to enter the respective value for First Acute Angle of Concave Quadrilateral, Third Acute Angle of Concave Quadrilateral & Second Acute Angle of Concave Quadrilateral 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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