Question : The sides $P Q$ and $P R$ of $\triangle P Q R$ are produced to points $S$ and $T$, respectively. The bisectors of $\angle S Q R$ and $\angle T R Q$ meet at $\mathrm{U}$. If $\angle \mathrm{QUR}=59^{\circ}$, then the measure of $\angle \mathrm{P}$ is:
Option 1: 31o
Option 2: 62o
Option 3: 41o
Option 4: 49o
Correct Answer: 62 o
Solution :
$\angle QUR = 90 - \frac{\angle P}{2}$
⇒ $\frac{\angle P}{2}= 90 - 59$
⇒ $\frac{\angle P}{2}= 31$
⇒ $\angle P = 2 × 31 = 62^{\circ}$
Hence, the correct answer is $ 62^{\circ}$.
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