Calculate CDE using the given information about a circle, cyclic quadrilateral, and tangent.

Here's a step-by-step solution for the geometry problem.

Given Information:

• O is the center of the circle.
• $\angle ADO = 37^\circ$.
• $\angle OCD = 45^\circ$. (Assuming $\angle LCD$ in the text is a typo for $\angle OCD$ based on the diagram).
• EC is a tangent to the circle at C.
• ABCD is a cyclic quadrilateral.
• EC = 7 cm, DE = 5 cm.

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Part a) i) Calculate $\angle CDE$, giving reasons.

Step 1: Find $\angle ADC$.
In $\triangle OAD$, OA = OD (radii), so it is an