Answer
$30^{\circ};\,30^{\circ}$
Work Step by Step
We recall that the sum of the measures of angles in a triangle is $180^{\circ}$
The angle measures of the big triangle are $30^{\circ}$, $90^{\circ}$, and $(x^{\circ}+y^{\circ})$. The sum of them must be $180^{\circ}$.
$\implies (x^{\circ}+y^{\circ})=180^{\circ}-(90^{\circ}+30^{\circ})=60^{\circ}$
Now, the angle measures of the small triangle are $60^{\circ}$, $90^{\circ}$ and $y^{\circ}$ and because their sum is $180^{\circ}$ , we get
$y^{\circ}=180^{\circ}-(90^{\circ}+60^{\circ})=30^{\circ}$
$\implies x^{\circ}=60^{\circ}-y^{\circ}=60^{\circ}-30^{\circ}=30^{\circ}$
