"Dangling" words or phrases are not always -ing participial phrases. A more general term is "dangling modifiers." Explain the ambiguities in the following:
(1) Having expressed his opinion that he proposal would not work, a quick vote was taken (W,165).
(2) Being the daughter of a millionaire, the boys pretended great romantic interest (W,165).
(3) Known as a persistent social climber, few worthwhile invitations were received (W,165).
(4) As an experienced grifter, many were cheated out of their money (W,165).
(5) Without a penny to his name, things were looking hopeless (W,165).
(6) Happy over her approaching wedding day, the years of waiting now seemed worthwhile (W,165).
(7) When dejected, a prayer often helps to regain one's sense of proportion (W,165).
(8) Having arrived late, the train had already departed (W,165).