Final answer:
To find the radian measure of an angle at the center of a circle, divide the arc length intercepted by the radius of the circle. In this case, the radian measure is approximately 1.89 radians.
Step-by-step explanation:
The radian measure of an angle at the center of a circle can be found by dividing the arc length intercepted by the radius of the circle. In this case, the radius is 64.0 cm and the arc length is 121 cm. To find the radian measure, we can use the formula Δθ = Δ.s / r, where Δθ is the angle of rotation, Δ.s is the arc length, and r is the radius.
Substituting the given values, we have Δθ = 121 cm / 64.0 cm. Simplifying the expression, we get Δθ = 1.89 radians. Therefore, the radian measure of the angle at the center of the circle is approximately 1.89 radians.