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The 3 parallel lines that cut the two transversals create 2 similar triangles.

The big triangle has adjacent sides with lengths (3+5) and (2 + x)

The small triangle has adjacent sides with lengths 3 and 2.

By Property of Similar Triangles we have our proportion:

(3+5) / 3 = (2+x) / 2

8 / 3 = (2 + x) / 2

16/3 - 2 = x

16/3 - 6/3 = 10/3 = x

x = 10/3

Answer Choice C.) x = 10/3

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