is the best way to differentiate the type of reaction that should be used (electrocyclic, cycloaddition, or sigmatropic) when only given one reactant?…

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In pericyclic reactions, what it is the best way to differentiate the type of reaction that should be used (electrocyclic, cycloaddition, or sigmatropic) when only given one reactant?  I am getting confused with what type of reaction to use and whether to open a cyclic molecule into a chain or close it into a ring.  I am specifically struggling with number 28. I have attached the questions in one image and the respective answers in another

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