Question

step 1: $m\angle abe = 110^\circ$ (given); step 2: $m\angle ebc = 70^\circ$ (linear pair (or triple)); find $m\angle bfc$ (value is 70°) and select a reason. the diagram shows points a, b, c, d on a straight line, with $\angle abe = 110^\circ$, $\angle ebc = 70^\circ$, and a line from c to f, with b connected to e.

Explanation:

Step1: Identify parallel lines/transversal

Lines $AB$ and $CD$ are parallel, $BC$ is a transversal, and $BF$ is a transversal creating alternate interior angles.

Step2: Match angle measure

$\angle EBC$ and $\angle BFC$ are alternate interior angles, so they are congruent.
$\text{m}\angle BFC = \text{m}\angle EBC = 70^\circ$

Step3: State the reason

Alternate interior angles formed by a transversal cutting parallel lines are congruent.

Answer:

$\text{m}\angle BFC = 70^\circ$, Reason: Alternate Interior Angles Theorem