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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