[tex]\Delta ABC\cong\Delta DEF[/tex] says that the triangles ABC and DEF are congruent, but moreover that the corresponding angle pairs (A, D), (B, E), and (C, F) are congruent.
This means [tex]m\angle A=m\angle D[/tex], so
[tex](x+17)^\circ=2x^\circ\implies x=17[/tex]
so that [tex]m\angle A=17^\circ+17^\circ=34^\circ[/tex] and [tex]m\angle D=2\times17^\circ=34^\circ[/tex].
