If δabc and δgef are congruent by the asa criterion, which pair of angles must be congruent?

ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal. If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent. 

The answer for the question above would be ∠CAB and ∠GEF. I hope this helps.