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 : If in $\triangle PQR$ and $\triangle DEF, \angle P=52^{\circ}, \angle Q=74^{\circ}, \angle R=54^{\circ}, \angle D=54^{\circ}, \angle E=74^{\circ}$ and $\angle F=52^{\circ}$, then which of the following is correct?

Option 1: $\triangle \mathrm{PQR} \sim \triangle \mathrm{FED}$

Option 2: $\triangle \mathrm{RQP} \sim \triangle \mathrm{FED}$

Option 3: $\triangle \mathrm{PRQ} \sim \Delta \mathrm{FED}$

Option 4: $\triangle \mathrm{PQR} \sim \triangle \mathrm{DEF}$

Question : $\triangle ABC$ is an isosceles triangle with AB = AC. If $\angle BAC=50^\circ$, then the degree measure of $\angle ABC$ is equal to:

Option 1: $70^\circ$

Option 2: $55^\circ$

Option 3: $60^\circ$

Option 4: $65^\circ$

Question : If $\triangle{PQR} \cong \triangle{STR}, \angle {Q}=50^{\circ}$ and $\angle {P}=70^{\circ}$ and ${PQ}$ is $8 {~cm}$. Which of the following options is NOT correct?

Option 1: $\angle {TSR}=80^{\circ}$

Option 2: $\angle {PRT}=60^{\circ}$

Option 3: ${PR}={RS}$

Option 4: ${TR}={RQ}$

Question : In an isosceles triangle, if the unequal angle is five times the sum of the equal angles, then each equal angle is:

Option 1: $45^\circ$

Option 2: $60^\circ$

Option 3: $15^\circ$

Option 4: $30^\circ$