Question

In the above sided figure , if QT perpendicular to PR , angle TQR = 40° and angle SPR = 30° , find x and y.

Answer 1

In triangle QTR,

Angle Q + angle T + angle R = 180°

40°+ 90°+ x = 180°

130° + x = 180°

x= 180°-130°

x = 50°

In triangle PSR

Angle P +angle S + angle R = 180°

30° + angle S + 50° = 180°

80° + angle S = 180°

Angle S = 180°- 80°

Angle S = 100°

Angle PSQ + angle PSR = 180°( linear

pair )

y + 100° = 180°

y = 180° -100°

y = 80°

Answer 2

Answer:

Step-by-step explanation:

Solution:-

In Δ QTR 

∠ TQR + ∠ QRT + ∠ QTR = 180°

⇒ 40° + y + 90° = 180°

⇒ y = 180° - 130°

⇒ y = 50°

∠ QSP = ∠ SPR + ∠ SRP

Reason : Exterior angle = sum of interior angles

⇒ x = 30° + y

⇒ x = 30° + 50°

⇒ x = 80°

So, ∠ x = 80° and ∠ y = 50°  Answer.

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