Joan has a piece of material for making a costume she needs to cut it as shown what is the angle measure of the piece left over?

We need to see the problem. show a picture

Two of the choices are correct: r corresponds to u. uv corresponds to rs. assuming that triangles srq and vut have their corresponding vertexes listed in the same order, we can look at the available options and see what makes sense. sq corresponds to vu. * nope. s is the 1st and q is the 3rd vertex for srq. but v is the 1st and u is the 2nd vertex. q does not correspond to u, so this is a bad choice. r corresponds to u. * both r and u are the 2nd vertex of their respective triangle. so this is a good choice. uv corresponds to rs. * both uv and rs are the 2nd and 1st vertex of their respective triangles. so this too is a good choice. s corresponds to t. * s is the 1st vertex, and t is the 3rd. they don't correspond, so this is a bad choice. qs corresponds to rs * both sq and rs belong to the same triangle. so this one is just plain silly and is a wrong choice. note: if the initial assumption is incorrect, then the answer given is incorrect. you really should have provided a diagram or figure so that the assumption could be verified.