To find the measure of angle $\angle EDC$, we analyze the geometry of the given circle and the angles involved. Let’s proceed step by step:

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Given:

1. $E, A, B, C, D$ are points on the circumference of a circle.
2. $\angle EAC = 72^\circ$.
3. $\angle AEB = 25^\circ$.

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Step 1: Use the Inscribed Angle Theorem

• The inscribed angle $\angle EAC$ subtends the same arc as $\angle EDC$ (both subtend arc $EC$).
• By the Inscribed Angle Theorem, $\angle EAC = \angle EDC$.

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Step 2: Conclude

Since $\angle EAC = 72^\circ$, we have:

$\angle EDC = 72^\circ$

Thus, $\angle EDC = 72^\circ$.

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Would you like a detailed explanation of how the Inscribed Angle Theorem works or help with related problems?

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5 Related Questions:

1. How is the Inscribed Angle Theorem applied in cyclic quadrilaterals?
2. Can the measure of other angles in this diagram be determined?
3. How can $\angle BCD$ be calculated from this configuration?
4. What is the relationship between central angles and inscribed angles?
5. Can the arcs in this circle be used to solve additional angle problems?

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Tip:

In cyclic quadrilaterals, opposite angles are supplementary. Always check if this property can simplify your calculations.