Question

If QT ⊥​ PR, ∠​TQR = 40° and ∠​SPR = 30°, Find x, y.​

Answer 1

$\textbf{\huge{\underline{Solution:-}}}$

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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°.

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Answer 2

Answer:

• x° = 50°
• y° = 80°

Step-by-step explanation:

Given

• QT⊥PR
• ∠TQR = 40°
• ∠SPR = 30°

To find

• x°
• y°

Solution

x° :-

• In ΔTQR,
• 90° + 40° + x° = 180°

(Angle sum property)

• 130° + x° = 180°
• x° = 180° - 130°
• x° = 50°

y° :-

• y° = ∠SPR + x°

(Exterior angle property)

• y° = 30° + 50
• y° = 80°

Hence, the value of x and y are 50° and 80° respectively.