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Besar sudut ECA diketahui sudut D=134° B=50°

Let's analyze the problem and find the measure of angle \( \angle ECA \).

### Given Information:
- \( \angle D = 134^\circ \)
- \( \angle B = 50^\circ \)
- We are looking for \( \angle ECA \).

### Solution Approach:
1. **Observe the Circle Properties**: Since the points \( D \), \( E \), \( C \), and \( A \) are on a circle, we can apply properties of cyclic quadrilaterals and inscribed angles.

2. **Inscribed Angle Theorem**: The angle subtended by the same arc at the circumference is half of the angle subtended at the opposite side. Also, in a cyclic quadrilateral, opposite angles sum up to \( 180^\circ \).

3. **Finding \( \angle DCA \)**:
   Since \( \angle B = 50^\circ \), we can deduce that \( \angle DCA = 50^\circ \) as both angles \( \angle B \) and \( \angle DCA \) subtend the same arc \( DA \).

4. **Using Triangle \( \triangle DCA \)**:
   - \( \angle D + \angle DCA + \angle ECA = 180^\circ \) (since it’s a triangle)
   - Substituting the values: \( 134^\circ + 50^\circ + \angle ECA = 180^\circ \)
   - \( 184^\circ + \angle ECA = 180^\circ \)
   - \( \angle ECA = 180^\circ - 184^\circ = 16^\circ \)

### Conclusion:
The measure of \( \angle ECA \) is \( 16^\circ \).

**Answer**: D. \( 16^\circ \)

Would you like further details on this solution or have any other questions?

### Related Questions:
1. What are the properties of cyclic quadrilaterals?
2. How do we use inscribed angles to find unknown angles in a circle?
3. What other methods can we use to solve angle problems in a cyclic quadrilateral?
4. How do opposite angles in a cyclic quadrilateral relate to each other?
5. How can we apply triangle angle-sum properties to find unknown angles?

### Tip:
In cyclic quadrilaterals, always remember that the sum of opposite angles is \( 180^\circ \). This property can simplify many angle-finding problems.

Solve the problem of finding the measure of angle ECA in a cyclic quadrilateral, given that angle D = 134° and angle B = 50°. Learn about circle theorems, cyclic quadrilaterals, and triangle angle sum properties.

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