Which sentence contains a dangling modifier?
a. upon bestowing the awards, the mayor congratulated all the participants.
b. upon hearing the fire engines, the apartment building was evacuated.
c. when operating heavy machinery, one must use caution.
d. upon taking the field, the player was hit by a foul ball.

The correct answer is B. Upon hearing the fire engines, the apartment building was evacuated.

A dangling modifier is a type of a modifier which is incorrectly placed within a sentence, or doesn't refer to anything. So, as you can see in the example above, the dangling modifier upon hearing the fire engines is incorrectly used - it would seem that the apartment heard the fire engines, whereas that is obviously not the case. 
A correct revision would be: Upon hearing the fire engines, the firefighters evacuated the apartment building.