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Lines and Angles

Short Answer Type

71. In figure, find the value of x.

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72. In figure, if QT ⊥ PR, ∠TQR = 40° and ∠SPR = 30°, find the value of x and y.

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73. In figure, if line segment AB intersects CD at O such that ∠OAD = 80°, ∠ODA = 50° and ∠OCB = 40°, then find ∠OBC.

In ∆OAD,
∠OAD + ∠ODA + ∠AOD = 180°
| Angle sum property of a triangle
⇒ 80° + 50° + ∠AOD = 180°
⇒    130° + ∠AOD = 180°
⇒ ∠AOD = 180° - 130° = 50°
⇒ ∠BOC = 50°
| ∵ ∠AOD = ∠BOC (Vertically opposite angles)
In ∆OBC,
∠BOC + ∠OCB + ∠OBC = 180°
| Angle sum property of a triangle ⇒ 50° + 40° + ∠OBC = 180°
⇒     90° + ∠OBC = 180°
∠    ∠OBC = 180° - 90° = 90°

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