Final answer:
Czech composer Antonín Dvořák's works of the 1870s, which include two sets of Slavonic Dances, often featured dumky and furiant movements.
Step-by-step explanation:
The works of the 1870s that include two sets of Slavonic Dances and that frequently employed dumky and furiant as inner movements of larger chamber and symphonic works were composed by the Czech composer Antonín Dvořák. Dvořák's Slavonic Dances were inspired by traditional Czech folk music and became immensely popular. They showcase rhythmic variety and melodic inventiveness, with the dumky, a melancholic Slavic folk ballad, and the furiant, a fast and fiery dance, being particularly distinct movements within his larger compositions.