Heeel

quadrilateral abcd is inscribed in this circle?

what is the measure of angle c?

Not to bore you to death with the "inscribed quadrilateral conjecture", but you can do a quick search on google for it.

to make it short the conjecture says, that if the quadrilateral is inscribed in a circle, opposite angles are "supplementary angles", namely in this case ∡D + ∡B = 180°, and ∡A + ∡C = 180°.