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The problem involves finding the measure of angle \( \angle AEC \) in the given geometric figure. The figure shows a circle with points \( A \), \( B \), \( C \), and \( E \) on its circumference, and \( AB \) is a chord of the circle.

### Solution:
1. **Identify the type of angle \( \angle AEC \):**
   - \( \angle AEC \) is an inscribed angle in the circle.

2. **Relation between inscribed angle and arc:**
   - The inscribed angle \( \angle AEC \) intercepts the arc \( AC \).
   - The measure of an inscribed angle is half the measure of the intercepted arc.

3. **Given information:**
   - In the figure, it seems that \( E \) is placed such that \( \angle AEB \) might be a straight line, making \( E \) the point of intersection of the extensions of \( AB \) and \( CD \). If \( AB \) is a diameter, then \( \angle ACB = 90^\circ \), and we might use properties of cyclic quadrilaterals or specific arcs if more information were given.

4. **Finding \( \angle AEC \):**
   - If \( AB \) is the diameter, then arc \( AC \) is 180°, meaning \( \angle AEC = \frac{1}{2} \times 180^\circ = 90^\circ \).
   - Therefore, \( \angle AEC \) is \( 90^\circ \).

The measure of \( \angle AEC \) is \( 90^\circ \).

Would you like more details or have any questions?

### Related Questions:
1. How can the properties of a cyclic quadrilateral be used to solve problems involving circles?
2. What is the relationship between an inscribed angle and the arc it intercepts?
3. How do we find angles in a circle when the chord is a diameter?
4. What is the significance of a diameter in a circle related to angles and arcs?
5. How does the concept of supplementary angles apply to cyclic quadrilaterals?

### Tip:
Remember that an inscribed angle is always half the measure of the intercepted arc. This is a fundamental property when working with problems involving circles.

Find the measure of angle \( \angle AEC \) in the given geometric figure where \( AB \) is a chord of the circle.

Learn how to find the measure of angle AEC in a circle, using the inscribed angle theorem. This problem involves key geometry concepts like inscribed angles, intercepted arcs, and circle theorems. Suitable for students in Grades 9-10.

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