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 : 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 $\triangle \mathrm{XYZ}$, I is the incentre of the $\triangle \mathrm{XYZ}$. If $\angle \mathrm{XYZ}=40$$^\circ$, then what is the value of $\angle \mathrm{XIZ}$?

Option 1: 110$^\circ$

Option 2: 130$^\circ$

Option 3: 115$^\circ$

Option 4: 120$^\circ$

Question : $\triangle PQR$ and $\triangle SQR$ are both isosceles triangles on a common base $QR$ such that $P$ and $S$ lie on the same side of $QR$. If $\angle QSR=60^{\circ}$ and $\angle QPR=100^{\circ}$, then find $\angle SRP$.

Option 1: $80^{\circ}$

Option 2: $60^{\circ}$

Option 3: $100^{\circ}$

Option 4: $20^{\circ}$

Question : In $\triangle {PQR}, {PN}$ is the median on ${QR}$. If ${PN}={QN}$, then what is the value of $\angle {QPR}$?

Option 1: $90^\circ$

Option 2: $80^\circ$

Option 3: $60^\circ$

Option 4: $75^\circ$