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How do you convert $ \dfrac{{4\pi }}{5} $ radians to degree?

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Last updated date: 22nd Jul 2024
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Answer
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Hint: Angle can be measured in radians or degrees. Radians and degrees are the units of the measure of the angle. Here, to Convert the given measure of angle radians into the degrees use the formula
 \[{\text{ Degree = }}\dfrac{{{\text{180}}^\circ }}{\pi } \times {\text{radians}}\]

Complete step-by-step answer:
Place the relation and simplify the equation using the basic mathematical calculations.
We know the basic relation between degrees and radians.
 \[{\text{ Degree = }}\dfrac{{{\text{180}}^\circ }}{\pi } \times {\text{radians}}\]
Place the value in the given value –
 \[{\text{ Degree = }}\dfrac{{{\text{180}}^\circ }}{\pi } \times \dfrac{{4\pi }}{5}\]
Simplifying the above equation, common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
Degree \[{\text{ = }}\dfrac{{{\text{180}}^\circ \times 4}}{5}\]
Find the factors for the term in the numerator –
Degree \[{\text{ = }}\dfrac{{36^\circ \times 5 \times 4}}{5}\]
Common factors from the numerator and the denominator cancel each other and therefore remove from the numerator and the denominator.
Degree \[{\text{ = }}36^\circ \times 4\]
Simplify the above expression finding the product of the terms
Degree \[{\text{ = 144}}^\circ \]
Hence, $ \dfrac{{4\pi }}{5} $ radians is \[144^\circ \] in degrees
This is the required solution.
So, the correct answer is “ \[144^\circ \]”.

Note: The units are the standards for the measurement of the physical quantities which needs to be clear to be useful. Internationally, the units are accepted standards for measurements of the physical quantities. Likewise angle of measure should be specified whether it is measured in degrees or radians since they both are different.