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.