jmc

For this problem, it is useful to know that the measure of an inscribed angle is half the measure of its corresponding central angle. Since each unit arc is $\frac{1}{12}$ of the circle's circumference, each unit central angle measures ${\left(\frac{360}{12}\right)}^{\circ }=30^{\circ }$. Then, we know that the central angle of x = $60$, so inscribed angle = $30$. Also, central angle of y = $120$, so inscribed angle = $60$. Summing both inscribed angles gives $30+60=\boxed{90}.$