Question

The perpendicular bisector of side AB of ∆ABC intersects side AB at point D and BC at point E. If m∠CAB = 82° and m∠C = 68°, find m∠CAE.

Answer 1

check the picture below.

now, an angle bisector I assume, since it intersects the opposite segment at D and then at E.  An angle bisector cuts an angle in two equal halves, so if ∡CAB is 82°, that just means that ∡CAE is one of those halves, or 41°.