Question : The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of $\angle PSR$ is:

Option 1: $30^{\circ}$

Option 2: $15^{\circ}$

Option 3: $60^{\circ}$

Option 4: $45^{\circ}$

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: $75^\circ$

Question : Three angles of a triangle are $(x-15^{\circ}),(x+45^{\circ}),$ and $(x+60^{\circ})$. Identify the type of triangle.

Option 1: Obtuse angle triangle

Option 2: Right angle triangle

Option 3: Isosceles triangle

Option 4: Equilateral triangle

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