Question : ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and $\angle A D C=148^{\circ}$. What is the measure of the $\angle BAC$?

Option 1: $32^{\circ}$

Option 2: $45^{\circ}$

Option 3: $58^{\circ}$

Option 4: $60^{\circ}$

Question : ABCD is a cyclic quadrilateral. The tangents to the circle at the points A and C on it, intersect at P. If $\angle\mathrm{ABC}=98^{\circ}$, then what is the measure of $\angle \mathrm{APC}$ ?

Option 1: 22°

Option 2: 26°

Option 3: 16°

Option 4: 14°

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 : The measure of three angles of a quadrilateral are in the ratio 1 : 2 : 3. If the sum of these three measures is equal to the measure of the fourth angle, then find the smallest angle.

Option 1: $30^\circ$

Option 2: $40^\circ$

Option 3: $60^\circ$

Option 4: $50^\circ$

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°