Any smooth curve connecting two points is called an arc. The measure of angle θ is (2/3)π radians.
Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,
Length of an Arc = 2π×R×(θ°/360°) = 2π×R×(θ/2π)
where
θ is the angle, that which arc creates at the centre of the circle in degree.
Given the length of OQ which is the radius of the circle is 9 inches, while the measure of arc PQ is 6π. Therefore, The measure of angle θ can be written as,
The length of arc = 2π×R×(θ/2π)
6π = 2π×9× (θ/2π)
θ = (2/3)π radians
Hence, the measure of angle θ is (2/3)π radians.
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