Describing Angles

We need to use the given diagram and that $m\angle BAC=70^{\circ }$ to find $m\angle HFI.$ To do so, we need to remember that angles that are congruent have equal measures. Consider the given diagram.

Congruent angles are marked with an arc. If there is more than one set of congruent angles, each set is marked with the same number of arcs. Since $\angle HFI$ and $\angle BAC$ are both marked with three arcs, they are congruent and they have the same measure. $$m\angle BAC=70=m\angle HFI$$