The sum of the lengths of CD and DE is 17α+13.
Based on the diagram you provided, we can see that CD and DE are adjacent segments on line CE. Therefore, the sum of their lengths is equal to the length of CE.
The length of CE is not given explicitly in the diagram, but we can infer it from the given information. We know that CD = 7α+11 and DE = 10α+2, so:
CE = CD + DE = 7α+11 + 10α+2 = 17α+13
Therefore, the sum of the lengths of CD and DE is 17α+13.
None of the answer choices match the correct answer of 17α+13. Therefore, the answer is None of the above.