Geometry Essentials · Superchallenge problem

Seven lines are drawn in a plane. Three of them are parallel to each other. Three others all pass through one point $P$, none of these three is parallel to the first three, and none of the first three passes through $P$. The seventh line is parallel to none of the others and does not pass through $P$, and no point other than $P$ lies on three or more of the lines. At every point where lines cross, count the pairs of vertical angles formed there (angles less than $180^\circ$ whose sides are opposite rays of each other). How many pairs of vertical angles are there in all?