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An arc has a length of 123.53 millimeters and a radius of 28 millimeters.

What is the measure of the angle of the sector in degrees? Round to the nearest degree.

Angle of sector = __________ Degrees

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Luv2Teach

Answer:

Step-by-step explanation:

The formula for the length of an arc is

[tex]L=\frac{\theta}{360}*2\pi r[/tex]

We have L = 123.53 and twice the radius as 56.  Filling in:

[tex]123.53=\frac{56\pi \theta}{360}[/tex]

Begin by multiplying both sides by 360 to get

[tex]44470.8=56\pi \theta[/tex]  and divide both sides by 56π to get

θ = 253°

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