Triangle angles sum to 180 degrees

Using the fact that the three angles of a triangle add up to $180^\circ$, find the measure of angle $a$ in the figure.

[Figure] Triangle $ABD$ has a segment $AC$ drawn from vertex $A$ down to point $C$ on the base $BD$, splitting it into two smaller triangles. At point $C$, the angle on the left-triangle side ($\angle ACB$) is $110^\circ$, and at vertex $A$ the angle of the right-hand triangle ($\angle CAD$) is $60^\circ$. The angle $a$ to be found is at vertex $D$.