Dangling modifiers are somewhat nuanced. To have a clearly dangling modifier, the modifier portion needs to clearly imply the action of an unnamed subject but the sentence itself does not mention that subject.
Arriving late for work, a meeting was missed.
In this case, some unnamed person seems to have arrived late for work and we would expect that person to be named directly after the modifying phrase, but instead the sentence implies that a meeting somehow arrived late?
The fix is simple - include the unnamed subject of the modifier:
Arriving late for work, I missed the meeting.
Now, you are absolutely correct that things get a bit muddy when we use the passive voice because the unnamed subject of the modifier would not appear after the modifier in passive voice. The question about whether you have a dangling modifier with passive voice is dependent upon the structure of the modifier itself - does it clearly imply an unnamed subject? In your examples about surgery performance using the latest technology, the phrase "using the latest technology" doesn't clearly imply a person. It could simply be a generalization about the type of surgery and how it now employs the latest technology. Both your examples are fine from a dangling modifier and passive voice standpoint.
Here is a variation of your surgery example that does imply an unnamed subject and therefore includes a dangling modifier:
Using both a computer display and x-ray images, a surgery was performed.
In the example above, we get the clear impression of a surgeon using the computer display and x-ray images, but the sentence itself (written in passive voice) does not name the surgeon. This is a dangling modifier.
In your last example, we can see that the modifier does not clearly imply an unnamed subject and therefore does not include a dangling modifier.
I hope that helps!
Kyle Widdison | Manhattan GMAT Instructor | Utah
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