Question : In $\triangle {ABC}$, D is a point on BC such that $\angle {ADB}=2 \angle {DAC}, \angle {BAC}=70^{\circ}$ and $\angle {B}=56^{\circ}$. What is the measure of $\angle A D C$?

Option 1: $72^{\circ}$

Option 2: $54^{\circ}$

Option 3: $74^{\circ}$

Option 4: $81^{\circ}$

Question : ABC is an isosceles triangle having AB = AC and $\angle$A = 40$^\circ$. Bisector PO and OQ of the exterior angle $\angle$ ABD and $\angle$ ACE formed by producing BC on both sides, meet at O, then the value of $\angle$BOC is:

Option 1: 70$^\circ$

Option 2: 110$^\circ$

Option 3: 80$^\circ$

Option 4: 55$^\circ$

Question : If $\triangle \mathrm{ABC} \cong \triangle \mathrm{PQR}, \mathrm{BC}=6 \mathrm{~cm}$, and $\angle \mathrm{A}=75^{\circ}$, then which one of the following is true?

Option 1: $\mathrm{QR}=6$ cm, $\angle \mathrm{R}=75^{\circ}$

Option 2: $\mathrm{QR}=6$ cm, $\angle \mathrm{Q}=75^{\circ}$

Option 3: $\mathrm{QR}=6$ cm, $\angle \mathrm{P}=75^{\circ}$

Option 4: $\mathrm{PR}=6$ cm, $\angle \mathrm{P}=75^{\circ}$

Question : $\angle A, \angle B$ and $\angle C$ are three angles of a triangle. If $\angle A- \angle B=15^{\circ}, \angle B - \angle C=30^{\circ}$, then $\angle A, \angle B$ and $\angle C$ are:

Option 1: $80^{\circ},60^{\circ},$ and $40^{\circ}$

Option 2: $70^{\circ},50^{\circ},$ and $60^{\circ}$

Option 3: $80^{\circ},65^{\circ},$ and $35^{\circ}$

Option 4: $80^{\circ},55^{\circ},$ and $45^{\circ}$

Question : In $\triangle A B C, \angle A=66^{\circ}$ and $\angle B=50^{\circ}$. If the bisectors of $\angle B$ and $\angle C$ meet at P, then, $\angle B P C-\angle P C A=$?

Option 1: $93^\circ$

Option 2: $91^\circ$

Option 3: $83^\circ$

Option 4: $81^\circ$