Cannot find the x and y angles. Is there something about the congruent lines in the two triangles that i need to use to find the answer? 
Got the triangle on the left as 60° 60° 60° and the middle angle at the bottom is 46° but that's about it. What am I missing to get X and Y?

Since the segments marked with a red | are the same length, the other two (nonequiangular) triangles in the picture are both isosceles.
$\Delta QST$ isosceles means both of the unknown angles in it have the same measure (i.e. both are $x^\circ$).  Thus, $x^\circ + x^\circ + 74^\circ = 180^\circ$.  Solving gives $x^\circ = 53^\circ$.
$\Delta QSP$ isosceles means the angles opposite its congruent sides are congruent angles, so you can find the unknown angles in $\Delta QSP$ using similar reasoning.
Bottom line:  If you know any one of the angles in an isosceles triangle you can figure out the other two.
