This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Step 1: Identify angles subtended by the same arc. The angle is . This angle is subtended by arc CD. The angle is . This angle is also subtended by arc CD.
Step 2: Apply the theorem that angles subtended by the same arc at the circumference are equal. Since and both subtend arc CD, their measures are equal.
Step 3: Identify another pair of angles subtended by the same arc. The angle is . This angle is subtended by arc AB. The angle is . This angle is also subtended by arc AB.
Step 4: Apply the theorem that angles subtended by the same arc at the circumference are equal. Since and both subtend arc AB, their measures are equal.
The values of and are:
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Identify angles subtended by the same arc. The angle 55^ is CAD.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.