Question : If P is circumcentre in $\triangle$ ABC, $\angle$BPC = $30^{\circ}$, what is the value (in degrees) of $\angle$BAC ?

Option 1: 15

Option 2: 60

Option 3: 75

Option 4: 105

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 : 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 : PQR is a triangle. The bisectors of the internal angle $\angle Q$ and external angle $\angle R$ intersect at S. If $\angle QSR=40^{\circ}$, then $\angle P$ is:

Option 1: $40^{\circ}$

Option 2: $60^{\circ}$

Option 3: $80^{\circ}$

Option 4: $30^{\circ}$

Question : If in $\triangle \mathrm{ABC}, \mathrm{AB}=\mathrm{AC}$ and $\angle \mathrm{ACD}=125^{\circ}$, then $\angle \mathrm{BAC}$ is:

Option 1: $75^\circ$

Option 2: $55^\circ$

Option 3: $60^\circ$

Option 4: $70^\circ$

Question : In $\triangle \mathrm{ABC}, \mathrm{BD} \perp \mathrm{AC}$ at D. E is a point on BC such that $\angle \mathrm{BEA}=x^{\circ}$. If $\angle \mathrm{EAC}=62^{\circ}$ and $\angle \mathrm{EBD}=60^{\circ}$, then the value of $x$ is:

Option 1: $92^\circ$

Option 2: $78^\circ$

Option 3: $76^\circ$

Option 4: $68^\circ$