A dangling modifier is a modifier without a headword - a word or phrase that it can modify. Since a modifier always needs a headword, it will attach itself to a false one if the true one is not present in the sentence. The result will be a sentence like this:
Listening to the sad news, my eyes filled with tears.
Here the sentence opens with a modifier - the participle phrase Listening to the sad news.After the modifier , there must be a headword naming the person(s) who did the listening.But instead we come across my eyes.As a result, the sentence seems to say that eyes heard some sad news .(The presence of my hints at the identity of the true headword , but my itself is not a headword.It is a modifier of eyes.).
To clarify the sentence,the writer can do one of two things - rewrite the word group following the modifier, or rewrite the modifier:
Edited A - Listening to the sad news, I felt my eyes filled with tears.
Edited B- As I listened to the sad news, my eyes filled with tears.
For Gmat example of Dangling modifier click on the link below view sentence 24
Dangling Modifier Link 1
Dangling modifier Link 2