Final answer:
The measure of angle θ is 150 degrees.
Step-by-step explanation:
To find the measure of angle θ, we can use the formula Δθ = 2s/r, where Δθ is the rotation angle, s is the arc length, and r is the radius of the circle. In this case, s = 5π/6 and r = 2. Plugging in these values, we have Δθ = 2(5π/6) / 2 = 5π/6 radians.
To convert radians to degrees, we use the conversion factor 180/π. Multiplying 5π/6 by 180/π, we get (5π/6)(180/π) = 150 degrees.
Therefore, the measure of angle θ is 150 degrees, which corresponds to option C) in the given choices.