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 : 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 a $\triangle ABC$, the bisectors of $\angle$ABC and $\angle$ACB intersect each other at point O. If the $\angle$BOC is 125°, then the $\angle$BAC is equal to:

Option 1: 75°

Option 2: 78°

Option 3: 70°

Option 4: 82°

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 a triangle, ABC, BC is produced to D so that CD = AC. If $\angle BAD=111^{\circ}$ and $\angle ACB=80^{\circ}$, then the measure of $\angle ABC$ is:

Option 1: 31°

Option 2: 33°

Option 3: 35°

Option 4: 29°