To solve this problem, let’s analyze the given information.

The problem states:

1. $\overline{AB}$ is congruent to $\overline{BC}$.
2. $\overline{AE}$ intersects $\overline{BF}$ at point $C$.
3. The angle $\angle ECF = 26^\circ$.
4. We are asked to find the measure of $\angle B$.

Solution:

Since $\overline{AB}$ is congruent to $\overline{BC}$, triangle $ABC$ is an isosceles triangle with $AB = BC$. In an isosceles triangle, the base angles are equal.

Let:

• $\angle ABC = \angle BAC = x$ (since $\triangle ABC$ is isosceles).

In a straight line, the sum of angles around point $C$ is $180^\circ$. Therefore, $\angle BCA + \angle ECF = 180^\circ$ Since $\angle ECF = 26^\circ$, $\angle BCA = 180^\circ - 26^\circ = 154^\circ.$

Now, in $\triangle ABC$, $\angle ABC + \angle BAC + \angle BCA = 180^\circ.$ Substituting the values: $x + x + 154^\circ = 180^\circ,$ $2x = 180^\circ - 154^\circ,$ $2x = 26^\circ,$ $x = 13^\circ.$

Thus, the measure of $\angle B$ is $13^\circ$.

Answer:

Since $13^\circ$ is not in the answer choices, it seems there might be a slight error in the setup or a reinterpretation is needed, but following the isosceles triangle properties, we arrive at $13^\circ$. Please verify the problem setup.

Would you like further explanation, or do you have questions about the geometry concepts used here?

Here are five related questions:

1. What is an isosceles triangle, and why are the base angles equal?
2. How do we calculate angles on a straight line?
3. Can you explain more about how to use the exterior angle theorem?
4. What properties define congruent segments in geometry?
5. How does angle-sum property help in solving triangle problems?

Tip: Always remember to verify that all problem conditions match real-life geometry setups.