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In the following figure, ΔPTQ an equilateral triangle and PQRS is a square, then find the value of ∠QRT + ∠PST = ?

In the following figure, ΔPTQ an equilateral triangle and PQRS is a square, then find the value of ∠QRT + ∠PST = ? Correct Answer 30°

Given,

ΔPTQ is an equilateral triangle.

PQRS is a square.

Formula:

Each angle of an equilateral triangle is 60°

Each angle of a square is 90°.

Calculation:

ΔPTQ is an equilateral triangle, then

PQ = PT = TQ      ---- (1)

PQRS is a square, then

PQ = QR = RS = SP     ---- (2)

From equation (1) and equation (2)

PQ = PT = TQ = QR = RS = SP

And, ∠TQP = 60° and ∠PQR = 90°

Now, ∠TQR = ∠TQP + ∠PQR

⇒ ∠TQR = 90° + 60° = 150°

In ΔTQR,

⇒ TQ = QR, then

⇒ ∠QTR = ∠QRT

⇒ ∠QTR + ∠QRT + ∠TQR = 180°

⇒ 2∠QRT + 150° = 180°

⇒ 2∠QRT = 180° - 150°

⇒ 2∠QRT = 30°

⇒ ∠QRT = 30°/2

⇒ ∠QRT = 15°

Similarly,

⇒ ∠PST = 15°

∴ ∠QRT + ∠PST = 15° + 15° = 30°

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