The question provided appears to involve a geometry problem related to a circle, chords, and angles. Let me extract the mathematical details and provide a solution.

Problem Interpretation:

1. There is a circle with points $A, B, C, D, E$ marked on it.
2. $\angle A$ is given as $37^\circ$, and $DME = 97^\circ$.
3. The question asks for the measure of the angle $CDE$ if $CD$ is the diameter.

Approach:

• Since $CD$ is the diameter of the circle, the angle subtended by the diameter at the circumference (like $CDE$) is a right angle, i.e., $90^\circ$.
• Using the given angles and properties of cyclic quadrilaterals, I can verify further calculations if needed.

Direct Calculation:

1. By the theorem, the angle subtended by the diameter is $90^\circ$.
2. Therefore, $\angle CDE = 90^\circ$.

The correct answer is $90^\circ$.

Let me know if you need further clarification on this or any related geometric concepts.

Follow-up Questions:

1. What is the relationship between a diameter and the angles it subtends at the circumference?
2. How does the angle sum property apply to cyclic quadrilaterals?
3. Can you explain the connection between central angles and inscribed angles?
4. What are other notable properties of angles in circles?
5. How can this theorem be applied to solve real-world geometric problems?

Tip: Always use key properties of circles, such as "angle subtended by a diameter is a right angle," to simplify geometric problems.