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Find the angle measure of $4 radians$ in $degree$ :

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114.591 °

141.372 °

229.183 °

282.743 °

458.366

answer is C.

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Detailed Solution

Concept- Use the fact that one complete rotation is equal to

2 π

radians and also equal to

360 °

. Use the unitary method to convert

4 radians

degrees

.
The angle subtended by the arc of length 1 unit at the center of a circle of radius 1 unit is said to be equal to

1 radian

. Hence in this system, one complete angle is equal to

2 π

radians.
We know that

2 π

radians are equal to

360 °

Then,

1 radian

is equal to

\frac{360 °}{2 π} = 180 ° π

So,

4 radians

are equal to

180 ° π \times 4 = 229.183 °

Therefore,

4 radians

are equal to

229.183 °

Hence, option 3 is correct.

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