Question : It is given that ABC $\cong$ PQR, AB = 5 cm, $\angle$B = $40^{\circ}$, and $\angle$A = $80^{\circ}$. Which of the following options is true?
Option 1: PQ = 5 cm and $\angle$R = $60^{\circ}$
Option 2: QR = 5 cm and $\angle$R = $60^{\circ}$
Option 3: QR = 5 cm and $\angle$Q = $60^{\circ}$
Option 4: PQ = 5 cm and $\angle$P = $60^{\circ}$
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Correct Answer: PQ = 5 cm and $\angle$R = $60^{\circ}$
Solution :
$\angle$C = $180^{\circ}-40^{\circ}-80^{\circ}$ = $60^{\circ}$
Since ABC $\cong$ PQR,
AB = PQ = 5 cm
$\angle$A = $\angle$P = $80^{\circ}$
$\angle$B = $\angle$Q = $40^{\circ}$
$\angle$C = $\angle$R = $60^{\circ}$
Hence, the correct answer is PQ = 5 cm and $\angle$R = $60^{\circ}$.
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