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What is the measure (in radians) of the central angle \(\theta\) in the circle below?

Enter an exact expression.

A circle with a radius of twelve centimeters. There are two radii that highlight a sector. The measure of the arc is fourteen \(\pi\) centimeters. The central angle is labeled \(\theta\).

Answer :

The measure of the central angle (θ) in radians is (7π) / 6.

To find the measure of the central angle (θ) in radians, use the formula:

θ = (arc length) / (radius)

Given:

Radius of the circle = 12 centimeters

Arc length = 14π centimeters

Substituting the values into the formula:

θ = (14π) / 12

Simplifying:

θ = (7π) / 6

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