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 : In $\triangle A B C $, AB and AC are produced to points D and E, respectively. If the bisectors of $\angle C B D$ and $\angle B C E$ meet at the point O, and $\angle B O C=57^{\circ}$, then $\angle A$ is equal to:

Option 1: 93°

Option 2: 66°

Option 3: 114°

Option 4: 57°

Question : The chord of a circle is equal to its radius. The angle subtended by this chord at the minor arc of the circle is:

Option 1: $75^{\circ}$

Option 2: $60^{\circ}$

Option 3: $150^{\circ}$

Option 4: $120^{\circ}$

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 : PA and PB are two tangents from a point P outside the circle with centre O. If A and B are points on the circle such that $\angle \mathrm{APB}=142^{\circ}$, then $\angle \mathrm{OAB}$ is equal to:

Option 1: 31°

Option 2: 58°

Option 3: 71°

Option 4: 64°