Quadrilateral angles sum to 360 degrees

Using the fact that the four angles of a quadrilateral add up to $360^\circ$, find the measure of angle $a$ in the figure.

[Figure] A quadrilateral rests at an angle with one vertex sitting on a straight line. Of its four interior angles, the top angle is $100^\circ$, the left angle is $80^\circ$, the right angle is $70^\circ$, and the bottom vertex's interior angle is labeled $b$. That bottom vertex lies on the straight line, and along the line — from left to right — are a $45^\circ$ angle, the quadrilateral's interior angle $b$, and angle $a$, which together form the straight angle $180^\circ$.