In congruent figures, corresponding angles have equal measures. true or false?

This is true

Think of two houses. If we say "the houses are identical" then the corresponding pieces must be the same (eg: the doors must be the same type out of the same material). In this analogy, the houses are the triangles, which are the overall structures. The doors are the angles since they are pieces of the overall structures. This is what CPCTC is saying

CPCTC = Corresponding Parts of Congruent Triangles are Congruent

Once again, the final answer is true.