In the figure below, \(\overline{AB}\) is congruent to \(\overline{BC}\), and \(\overline{AE}\) intersects \(\overline{BF}\) at \(C\). What is the measure of \(\angle{B}\) ?

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The two angles opposite at point \(C\) are vertical angles and therefore congruent.

\(\triangle{ABC}\) is isosceles since two of its sides are congruent. \(\angle{A}\) will be congruent to \(\angle{ACB}\).

For the three angles in \(\triangle{ABC}\):

$$ m\angle{A} + m\angle{B} + m\angle{C} = 180^\circ $$ $$ 26^\circ + m\angle{B} + 26 = 180^\circ $$ $$ 52^\circ + m\angle{B} = 180^\circ $$ $$ m\angle{B} = \boxed{128^\circ} $$