In the figure below, AB is congruent to BC, and AE intersects BF
at C. What is the measure of ∠B ?
The two angles opposite at point C are vertical angles and therefore congruent.
△ABC is isosceles since two of its sides are congruent. ∠A will be congruent to ∠ACB.
For the three angles in △ABC:
m∠A+m∠B+m∠C=180∘
26∘+m∠B+26=180∘
52∘+m∠B=180∘
m∠B=128∘