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?
 A: You are essentially missing the fact the sum of the inner angles of any triangle equals $180°$.
Notice that $y° = 180° - 2\times(180° - 60° - 74°) = 180° - 2\times 46° = 88°$.
Hence the right answer is given by the letter (B).
Hopefully this helps!
EDIT
To begin with, notice that
\begin{align*}
\angle PQR + \angle PQS + \angle SQT = 180° \Rightarrow \angle PQS & = 180° - \angle PQR - \angle SQT\\\\
& = 180° - 60° - 74° = 46°
\end{align*}
That is because the triangle $\Delta PRQ$ is equiangular and the angle $\angle SQT$ is given.
Since the triangle $\Delta SPQ$ is isosceles, it results that $\angle PQS = \angle QPS = 46°$.
Based on such information, one concludes that $y° = 180° - 2\times 46° = 88°$, and we are done.
A: 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.
