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°

Question : ${L}$ is the incentre of $\triangle ONP$. If $\angle {OLP}+\angle {ONP}=195^\circ$, then what will be the value of $\angle {OLP}$?

Option 1: $115^\circ$

Option 2: $140^\circ$

Option 3: $135^\circ$

Option 4: $125^\circ$

Question : If $ABCD$ is a cyclic quadrilateral with $\angle A=50^{\circ},\angle B=80^{\circ}$, then $\angle C$ and $ \angle D$ are:

Option 1: $100^{\circ}$ and $130^{\circ}$

Option 2: $115^{\circ}$ and $115^{\circ}$

Option 3: $110^{\circ}$ and $120^{\circ}$

Option 4: $130^{\circ}$ and $100^{\circ}$

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?

Option 1: $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$

Option 2: $\triangle \mathrm{RQP} \sim \triangle \mathrm{FED}$

Option 3: $\triangle \mathrm{PRQ} \sim \Delta \mathrm{FED}$

Option 4: $\triangle \mathrm{PQR} \sim \triangle \mathrm{DEF}$

Question : $\mathrm{O}$ is the centre of a circle and $\mathrm{A}$ is a point on a major arc $\mathrm{BC}$ of the circle. $\angle \mathrm{BOC}$ and $\angle \mathrm{BAC}$ are the angles made by the minor arc $\mathrm{BC}$ on the centre and circumference, respectively. If $\angle \mathrm{ABO}=40^{\circ}$ and $\angle \mathrm{ACO}=30^{\circ}$, then find $\angle \mathrm{BOC}$.

Option 1: $130^{\circ}$

Option 2: $140^{\circ}$

Option 3: $120^{\circ}$

Option 4: $150^{\circ}$