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the diameter of a circle is 8 cm.. a central angle of the circle intercepts an arc 12 cm in length. find to the nearest degree to measure of the angle

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Answer:

The measure of the angle is 172 degrees

Step-by-step explanation:

The diameter of the circle is 8 cm

Because the radius is half of the diameter, we have:

Radius (r) = 4 cm

The arc length is the product of the angle and the radius:

L = rθ

The length is given as 12 cm, so we have:

12 = 4θ

Divide both sides by 4

θ = 12/4 = 3

The angle measures 3 radians

We need to convert this to degrees:

Note that:

1 degree = π/180 radians

So, we divide 3 by π/180 to obtain the value in degrees

This is 171.887

Approximately 172 degrees

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