In each of the sentences below, the subject of the main clause is not logically associated with the subordinate clause, so the former must be recast to begin with the noun or pronoun in the sentence that the latter applies to, or the sentence must be revised so that a subject that pertains to the additional information provided at the head of the sentence replaces the inapt noun or pronoun. Discussion following each example explains the unsuitably of the existing subject, and revisions demonstrate how the sentences can be repaired.
1. Broken by unresolved trauma, the apocalypse is slowly wearing her down.
The person referred to, not the apocalypse, is broken by unresolved trauma, so she must be the subject of the main clause: “Broken by unresolved trauma, she is slowly being worn down by the apocalypse.”
2. As a valued customer of World Wide Wickets, we would like to extend an invitation to you to view some exclusive deals on our products.
Because we is the first word that follows the subordinate clause, the erroneous implication is that the entity self-described as “we” is a valued customer of the company, so the sentence must be recast to place the entity “you” in that role; the “we” can safely be omitted: “As a valued customer of World Wide Wickets, you are cordially invited to view some exclusive deals on our products.”
3. Appearing on the cover of Time magazine in 1994, tales of his exploits on the job turned him into a local legend.
This sentence implies that tales of a person’s exploits appeared on the cover of the magazine, but it was he himself who appeared on the cover, and the role of the tales in turning him into a local legend is a separate matter: “He appeared on the cover of Time magazine in 1994, and tales of his exploits on the job turned him into a local legend.”
Seeing examples of dangling modifiers repeatedly, my annoyance with their ubiquity rose.
There. I dangled. But am I annoyed with the ubiquity of the examples of of the dangles?