Question : In $\triangle P Q R$, $\angle Q=90^{\circ}$, $PQ=8$ cm and $\angle P R Q=45^{\circ}$ Find the length of $QR$.
Option 1: 6 cm
Option 2: 3 cm
Option 3: 5 cm
Option 4: 8 cm
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Correct Answer: 8 cm
Solution :
Putting all the given values, we get,
$\angle PQR +\angle PRQ + \angle RPQ = 180°$
$90° + 45°+\angle RPQ = 180°$
$\therefore \angle RPQ= 45°$
⇒ PQR is an isosceles triangle.
$\therefore$ PQ = QR = 8 cm
Hence, the correct answer is 8 cm.
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