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A puzzle: A transversal meets two lines, and the two interior angles on the SAME side are supplementary (sum 180°). The same transversal meets two OTHER lines where the corresponding interior angles on the same side sum to 175°.
For which pair are the lines parallel, and what happens to the other pair?

Class 9The Fifth PostulateGeometry — Foundations
  • AFirst pair is parallel; the second pair meets (since 175° < 180°)
  • BSecond pair is parallel; first pair meets
  • CBoth pairs are parallel
  • DNeither pair is parallel

Step-by-Step Solution

Sum 180° means parallel (first pair). Sum 175° < 180° means, by the fifth postulate, the lines meet on that side (second pair).
Answer: A) First pair is parallel; the second pair meets (since 175° < 180°)

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