(a) Draw in radii OA, OB, OC and OD. Then, explain why OAB must
be congruent to ODC.

(b) Given that OAB is congruent to ODC, why can we now say that mAB = mCD?

In the given circle, segments OA, OB, OC and OD are radius of the circle.

In other words, all those segments are congruent.

From that we can deduct that triangles OAB and OCD are isosceles triangles, because all segments are equal. That makes those triangles congruent, because they have the same sides.

From the congruence we can deduct that all corresponding internal angles inside those triangles are actually congruent, that's why angle OAB and ODC must be congruent.

Also, angles DOC and BOA are also congruent, which means their subtended arcs are also congruent, because they have the same radius, so mAB = mCD.