Question

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

- 160°
- 85°
- 35°
- 55°

Hint:

### 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 = x ∠OSR

⇒ ∠SRO = x 100°

⇒ ∠SRO = 75°

Also, ∠OSR + ∠SRO + ∠ROS = 180° (Angle Sum property of triangle)

⇒ 50° + 75° + ∠ROS = 180°

⇒ ∠ROS = 180° – 125°

⇒ ∠ROS = 55°.

In ∆ SOR, ∠OSR: ∠SRO = 2: 3

⇒ ∠SRO = x ∠OSR

⇒ ∠SRO = 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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