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A transversal crosses two straight lines so that the interior angles on the same side are 85° and 88°.
By Euclid's fifth postulate, do the two lines meet on that side when produced?

Class 9Euclid's PostulatesGeometry — Foundations
  • AYes, because 85 + 88 = 173° is less than 180°
  • BNo, because the angles are unequal
  • CNo, the lines are always parallel
  • DYes, because 85 + 88 is more than 180°

Step-by-Step Solution

Sum of co-interior angles = 173° < 180 deg (two right angles), so by the fifth postulate the lines meet on that side.
Answer: A) Yes, because 85 + 88 = 173° is less than 180°

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