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Lines and Angles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsLines and Angles1 Mark
MCQ
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 larger angle is:
  • A
    54°
  • B
    120°
  • C
    108°
  • D
    136°
✓

Answer

  1. 108°
    Solution:

    Let AB and CD are two parallel lines and PQ is transverce to it.
    According to question,
    $\frac{\angle\text{BRS}}{\angle\text{DSR}}=\frac{2}{3}$
    $\Rightarrow\ \angle\text{BRS}=\frac{2}{3}\angle\text{DSR}\dots(1)$
    Now,
    $\angle\text{CSR}=\angle\text{BRS}$ [Alternate angles]
    $\Rightarrow\ \angle\text{CSR}+\angle\text{DSR}=180^\circ$
    $\Rightarrow\ \angle\text{BRS}+\angle\text{DSR}=180^\circ$
    $\Rightarrow\ \frac{2}{3}\angle\text{DSR}+\angle\text{DSR}=180^\circ$
    $\Rightarrow\ \angle\text{DSR}=\frac{180\times3}{5}=108^\circ$
    $\Rightarrow\ \angle\text{BRS}=\frac{2}{3}\times108^\circ=72^\circ$
    Thus,
    $\angle\text{DSR}=108^\circ$ and $\angle\text{BRS}=72^\circ$
    ⇒ Larger angle is $\angle\text{DSR}.$

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