Final answer:
Kyle would likely use the head of household filing status in 2017 since he maintains a home for his dependent children and has not remarried.
Step-by-step explanation:
Kyle's filing status in 2017, assuming he has not remarried and continues to maintain a home where his two dependent children live, would likely be head of household. He cannot file as a surviving spouse because this status is generally only available for two tax years following the year of the spouse's death.
Therefore, as of 2017, the qualifying widow/widower status would no longer apply. He is not married, so he cannot file as married filing separately, and because he has dependents and maintains a household, he does not file as single. The head of household status offers more favorable tax rates and a higher standard deduction than the single filing status.