The clocks

Tim has a working analog 12-hour clock with two hands that run continuously (instead of, say, jumping
on the minute). He also has a clock that runs really slow—at half the correct rate, to be exact. At
noon one day, both clocks happen to show the exact time. At any given instant, the hands on each
clock form an angle between 0 and 180 inclusive. At how many times during that day are the angles
on the two clocks equal