A tangential /c-block over GF(q) is a simple matroid representaba over GF(q) with critical exponent k + 1 for which every proper loopless minor has critical exponent at most k. Such matroids are of central importance in the critical problem of Crapo and Rota. In this paper we provide sufficient conditions for a quotient of a tangential fc-block over GF(q) to be also a tangential fc-block over GF{q). This enables us to show that there exist rank r supersolvable tangential fc-blocks over GF(q) exactly when qk > r > k + 1.