Lines and Angles · Class 9 · CBSE Mathematics

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then the measure of the smaller angle…

Practice question from Lines and Angles (Class 9 · CBSE Mathematics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-394523

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2:3, then the measure of the smaller angle is:

  1. A.54°
  2. B.72°Correct answer
  3. C.108°
  4. D.36°

Solution

Let the two interior angles on the same side of the transversal be 2x2x and 3x3x. We know that consecutive interior angles for parallel lines are supplementary, so 2x+3x=180∘2x + 3x = 180^\circ. This gives 5x=180∘5x = 180^\circ, or x=36∘x = 36^\circ. The smaller angle is 2x=2×36∘=72∘2x = 2 \times 36^\circ = 72^\circ.

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