In figure, if QT ⊥ PR, ∠TQR = 40° and ∠SPR = 30°, find t

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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.

In ∆QTR,
∠QTR + ∠r + 40° = 180°
| ∠ Angle sum property of a triangle
⇒ 90° + ∠x + 40° = 180°
⇒ ∠r + 130° = 180°
⇒ ∠x = 180° - 130° = 50°
∠x = 50°
In ∠PSR,
y° = x° + 30°
| Exterior angle theorem
= 50° + 30°
= 80°
⇒ y = 80°

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Long Answer Type

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Short Answer Type

78. In figure, PS is the bisector of ∠QPR and PT ⊥ QR. Show that

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