Question

Given circle O with s=5π6, r=2 inches, find the measure of angle θ.

A) 120 degrees

B) 135 degrees

C) 150 degrees

D) 180 degrees

Answer 1

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.