Question

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 = __________

Answer 1

Answer:

Step-by-step explanation:

The formula for arc length in terms of degrees is

$A.L.=\frac{\theta}{360}*2\pi r$ and we have everything we need to fill in to find the angle measure.

$123.53=\frac{\theta}{360}*56\pi$ which is the same as

$123.53=\frac{56\pi \theta}{360}$ and

$360(123.53)=56\pi \theta$ and

$\frac{360(123.53)}{56\pi}=\theta$ so

θ = 253°