Question : In $\triangle \mathrm{PQR}, \angle \mathrm{P}=46^{\circ}$ and $\angle \mathrm{R}=64^{\circ}$.If $\triangle \mathrm{PQR}$ is similar to $\triangle \mathrm{ABC}$ and in correspondence, then what is the value of $\angle \mathrm{B}$?
Option 1: 70°
Option 2: 90°
Option 3: 100°
Option 4: 110°
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Correct Answer: 70°
Solution : $\angle$P = 46$^{\circ}$ $\angle$R = 64$^{\circ}$ In correspondence with $\triangle$PQR, we have $\triangle$ABC. Let's denote the corresponding angles of $\triangle$ABC as $\angle$A, $\angle$B, and $\angle$C. According to the property of similar triangles, the corresponding angles of similar triangles are equal. So, $\angle$P = $\angle$A $\angle$Q = $\angle$B $\angle$R = $\angle$C Using the given angle measures, we have: $\angle$P = $\angle$A = 46$^{\circ}$ $\angle$Q = $\angle$B $\angle$R = $\angle$C = 64$^{\circ}$ $\because$ The sum of angles in a triangle is 180°, $\angle$Q = 180$^{\circ}$ - $\angle$P - $\angle$R $\angle$Q = 180$^{\circ}$ - 46$^{\circ}$ - 64$^{\circ}$ $\angle$Q = 70$^{\circ}$ $\therefore$ The value of $\angle$B is 70$^{\circ}$ Hence, the correct answer is 70$^{\circ}$.
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Question : If in $\triangle PQR$ and $\triangle DEF, \angle P=52^{\circ}, \angle Q=74^{\circ}, \angle R=54^{\circ}, \angle D=54^{\circ}, \angle E=74^{\circ}$ and $\angle F=52^{\circ}$, then which of the following is correct?
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