Question : In $\triangle \mathrm{ABC}, \angle \mathrm{A}=54^{\circ}$. If I is the incentre of the triangle, then the measure of $\angle \mathrm{BIC}$ is:

Option 1: 68^o

Option 2: 54^o

Option 3: 148^o

Option 4: 117^o

Question : In a $\triangle \mathrm{ABC}$, the bisectors of $\angle \mathrm{B}$ and $\angle \mathrm{C}$ meet at $\mathrm{O}$. If $\angle \mathrm{BOC}=142^{\circ}$, then the measure of $\angle \mathrm{A}$ is:

Option 1: $52^\circ$

Option 2: $68^\circ$

Option 3: $104^\circ$

Option 4: $116^\circ$

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 : In $\triangle$ABC, $\angle$A = 66°. AB and AC are produced at points D and E, respectively. If the bisectors of $\angle$CBD and $\angle$BCE meet at the point O, then $\angle$BOC is equal to:

Option 1: $66^{\circ}$

Option 2: $93^{\circ}$

Option 3: $57^{\circ}$

Option 4: $114^{\circ}$

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°