A participle has the form of verb + -ing. So the only such word here is 'smiling' that is the participle in this sentence. It modifies 'woman', that is, it refers to how the woman opened the door - smiling pleasantly.
When writing the conclusion of an essay comparing different genres, it would be advisable to end up it by stating a summary of the main points of comparison and contrast. The conclusion should start by giving a brief, general summary of the points which have been covered in the body paragraphs.
<u>Answer:</u>
<em>A. He tells the Cyclops his name even though it risks the lives of his men.</em>
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<u>Explanation:</u>
The detail from the Odyssey which best shows that Odysseus can be vain is that there are unnecessary risks which are taken by him endangering his crew members so that he taunt the cyclops. The state of Ithaca is also entailed in the details of Odyssey. There are certain risks which are taken by him and goes in vain as they are of no use to him and in the plot construction and his actions.
Your answer is B. Look it up, you will see I am right.