Question : In $\Delta ABC$, the external bisector of the angles, $\angle B$ and $\angle C$ meet at the point $O$. If $\angle A = 70^\circ$, then the measure of $\angle BOC$:

Option 1: $55^\circ$

Option 2: $75^\circ$

Option 3: $60^\circ$

Option 4: $50^\circ$

Question : AB and BC are two chords of a circle with centre O. Both chords are on either side of the centre O. Point A and point C are connected to the centre O, such that $\angle B A O=36^{\circ}$ and $\angle B C O=48^{\circ}$. What is the degree measure of the angle subtended by the minor arc AC at the centre O?

Option 1: 136°

Option 2: 144°

Option 3: 120°

Option 4: 168°

Question : In $\triangle ABC$, the internal bisectors of $\angle B$ and $\angle C$ meet at point $O$. If $\angle A = 80^\circ$, then $\angle BOC$ is equal to:

Option 1: $100^\circ$

Option 2: $120^\circ$

Option 3: $130^\circ$

Option 4: $140^\circ$

Question : If in a $\triangle$PQR, $\angle$P = $88^\circ$, PQ and PR are produced to points S and T respectively. If the bisectors of $\angle$SQR and $\angle$TRQ meet at the point O. Find $\angle$QOR.

Option 1: $42^\circ$

Option 2: $46^\circ$

Option 3: $44^\circ$

Option 4: $48^\circ$

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: $150^{\circ}$