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In this geometry problem, we are given a configuration of triangles with known angles and are asked to find the value of \( x \), which is the angle at point \( C \) in triangle \( CED \). The diagram also states that points \( A \), \( D \), and \( E \) are collinear.

### Key information:
- \( \angle ABC = 26^\circ \)
- \( \angle ABD = 24^\circ \)
- \( \angle ABE = 30^\circ \)
- \( \angle ACD = 28^\circ \)
- \( \angle AEC = 40^\circ \)
- Points \( A \), \( D \), and \( E \) are collinear.

Let’s solve for \( x \) step by step.

### 1. Analyze the angles in the triangles:
Since points \( A \), \( D \), and \( E \) are collinear, the angles along the line \( ADE \) must sum to \( 180^\circ \).

For triangle \( CED \), we know:
- The sum of the interior angles of a triangle is \( 180^\circ \).
- We already know two angles: \( \angle EDC \) and \( \angle DCE \).
- We need to use this fact along with the given angles to determine \( x \).

### I'll now compute the missing values.The value of \( x \), the missing angle at \( C \) in triangle \( CED \), is \( 112^\circ \).

Would you like more details on any part of this solution, or do you have further questions?

Here are five related questions to deepen your understanding:
1. How do we determine the sum of interior angles in any triangle?
2. Why does the collinearity of points \( A \), \( D \), and \( E \) matter in this problem?
3. Can you prove that the exterior angle theorem holds for this triangle?
4. How would the solution change if one of the angles at \( B \) were different?
5. What role does symmetry play in problems like these?

**Tip:** In geometric problems involving collinear points, always consider the supplementary angles formed along the straight line.

Find the missing angle x in a triangle configuration where points A, D, and E are collinear, and angles at points B and C are provided. The given angles are as follows: 26°, 24°, 30°, 28°, and 40°.

Solve a geometry problem involving triangles and collinear points, using the sum of angles in a triangle and the exterior angle theorem. The diagram provides several angle measurements, and the task is to find the missing angle x.

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