Step 1 :Given that the measure of arc AB is 124 degrees and the measure of angle BPA is 32 degrees.
Step 2 :First, we find the measure of arc APB by subtracting the measure of arc AB from 360 degrees, which is \(360^{\circ} - 124^{\circ} = 236^{\circ}\).
Step 3 :Then, we find the measure of arc CD by subtracting the measure of arc APB and the measure of angle BPA from 360 degrees, which is \(360^{\circ} - 236^{\circ} - 32^{\circ} = 92^{\circ}\).
Step 4 :\(\boxed{92}\) is the measure of arc CD. However, this answer is not among the options provided. There might be a mistake in the problem or in the calculations.