Question : In $\Delta PQR,$ $\angle P : \angle Q : \angle R = 1: 3 : 5$, what is the value of $\angle R - \angle P$?

Option 1: $30^\circ$

Option 2: $80^\circ$

Option 3: $45^\circ$

Option 4: $60^\circ$

Question : Internal bisectors of $\angle$ B and $\angle$ C of $\triangle$ ABC meet at O. If $\angle$ BAC = $80^{\circ}$, then the value of $\angle$ BOC is:

Option 1: $120^{\circ}$

Option 2: $140^{\circ}$

Option 3: $110^{\circ}$

Option 4: $130^{\circ}$

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: 31^o

Option 2: 62^o

Option 3: 41^o

Option 4: 49^o

Question : In a $\triangle P Q R, \angle P=90^{\circ}, \angle R=47^{\circ}$ and $P S \perp Q R$. Find the value of $\angle Q P S$.

Option 1: 43°

Option 2: 47°

Option 3: 45°

Option 4: 40°

Question :
In the figure, in $\triangle {PQR}, {PT} \perp {QR}$ at ${T}$ and ${PS}$ is the bisector of $\angle {QPR}$. If $\angle {PQR}=78^{\circ}$, and $\angle {TPS}=24^{\circ}$, then the measure of $\angle {PRQ}$ is:
 

Option 1: 42$^{\circ}$

Option 2: 39$^{\circ}$

Option 3: 30$^{\circ}$

Option 4: 40$^{\circ}$