Question : It is given that $\triangle \mathrm{PQR} \cong \triangle \mathrm{MNY}$ and $PQ=8\ \mathrm{cm}, \angle Q = 55°$ and $\angle P = 72°$. Which of the following is true?
Option 1: $\mathrm{NY}=8 \mathrm{~cm}, \angle \mathrm{Y}=72^{\circ}$
Option 2: $\mathrm{NM}=8 \mathrm{~cm}, \angle \mathrm{M}=53^{\circ}$
Option 3: $\mathrm{NM}=8 \mathrm{~cm}, \angle \mathrm{Y}=53^{\circ}$
Option 4: $\mathrm{NY}=8 \mathrm{~cm}, \angle \mathrm{N}=55^{\circ}$
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Correct Answer: $\mathrm{NM}=8 \mathrm{~cm}, \angle \mathrm{Y}=53^{\circ}$
Solution :
In $\triangle PQR,$
$\angle P + \angle Q +\angle R = 180°$
⇒ $72°+55°+\angle R = 180°$
⇒ $\angle R = 180° - 127°$
⇒ $\angle R = 53°$
As $\triangle \mathrm{PQR} \cong \triangle \mathrm{MNY}$,
⇒ $\angle Y = \angle R=53° $ and $NM = PQ=8\ \mathrm{cm}$
Hence, the correct answer is $\mathrm{NM}=8 \mathrm{~cm}, \angle \mathrm{Y}=53^{\circ}$.
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