Answer
m$\angle$A$\lt$m$\angle$C
Work Step by Step
Since arc CD is smaller than arc AB, there corresponding central angles must have the same relationship. DQC and BQA are both isosceles triangles with radii for congruent sides. As the vertex of an isosceles triangle gets bigger, its base angles get smaller. Since the vertex angle AQB is larger than DQC, then base angle A must be smaller than base angle C.
