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

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

∠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∠QTR + 150° = 180°

⇒ 2∠QTR = 180° - 150°

⇒ 2∠QTR = 30°

⇒ ∠QTR = 30°/2

⇒ ∠QTR = 15°

Similarly,

⇒ ∠PTS = 15°

⇒ ∠PTQ = ∠PTS + ∠STR + ∠QTR

⇒ 60° = 15° + ∠STR + 15°

⇒ ∠STR = 60° – 30°

∴ ∠STR = 30°

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