AA' and BB' are two parallel straight lines. CC' is a transversal that intersects AA' and BB' at points D and E respectively. If ∠B'EC' = 127° and ∠CDA' = (7x − 3)°, find the value of x.
8
When transversal CC' cuts the parallel lines AA' and BB' at D and E respectively, the angles ∠CDA' (at D, interior to the two parallels on the A'-side) and ∠B'EC' (at E, interior to the two parallels on the B'-side) lie on opposite sides of the transversal between the parallel lines, so they are co-interior (same-side interior) with respect to the pair of angles on the same side of CC'.
From the geometry of parallel lines, the two angles ∠CDA' and ∠B'EC' are supplementary, i.e., their sum equals 180°. Therefore (7x − 3)° + 127° = 180°.
Solving: 7x − 3 = 180 − 127 = 53, so 7x = 56 and x = 8. Verification: with x = 8, (7×8 − 3)° = 53°, and 53° + 127° = 180°, which is consistent with parallel-line angle properties.
Hence, the correct answer is 8.
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