Mathematics
Grade9
Easy

Question

Find the angle SOR if PQ || RS and OSR: SRO = 2: 3.

  1. 160°
  2. 85°
  3. 35°
  4. 55°

hintHint:

Using Alternate Interior Angles at transversal are equal and given ratio find ∠SRO  and ∠OSR and find SOR  using sum of angles in a triangle is 180 degrees.

The correct answer is: 55°


    PQ || RS ⇒ ∠QPS = ∠PSR = 50° (Alternate Interior Angles)
    In ∆ SOR, ∠OSR: ∠SRO = 2: 3
    ⇒ ∠SRO = 3 over 2 x ∠OSR
    ⇒ ∠SRO = 3 over 2 x 100°
    ⇒ ∠SRO = 75°
    Also, ∠OSR + ∠SRO + ∠ROS = 180° (Angle Sum property of triangle)
    ⇒ 50° + 75° + ∠ROS = 180°
    ⇒ ∠ROS = 180° – 125°
    ⇒ ∠ROS = 55°.

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