Question : In $\triangle {PQR} $, PQ = PR and S is a point on QR such that $\angle {PSQ}=96^{\circ}+\angle {QPS}$ and $\angle {QPR} = 132^{\circ}$. What is the measure of $\angle {PSR}$?

Option 1: 45°

Option 2: 56°

Option 3: 54°

Option 4: 52°

Question : S and T are points on the sides PQ and PR, respectively, of $\triangle$PQR such that PS × PR = PQ × PT. If $\angle$Q = 96° and $\angle$PST = $\angle$PRQ + 34°, then $\angle$QPR = ?

Option 1: 24°

Option 2: 25°

Option 3: 22°

Option 4: 26°

Question : $\triangle \mathrm{PQR}$ is an equilateral triangle inscribed in a circle. $\mathrm{S}$ is any point on the arc $\mathrm{QR}$. Find the measure of $\angle \mathrm{PSQ}$.

Option 1: $30^{\circ}$

Option 2: $60^{\circ}$

Option 3: $90^{\circ}$

Option 4: $45^{\circ}$

Question : In $\triangle P Q R, S$ is a point on the side QR such that $\angle Q P S=\frac{1}{2} \angle P S R, \angle Q P R=78^{\circ}$ and $\angle P R S=44^{\circ}$. What is the measure of $\angle PSQ$?

Option 1: 68$^{\circ}$

Option 2: 56$^{\circ}$

Option 3: 58$^{\circ}$

Option 4: 64$^{\circ}$

Question : In triangle PQR, the sides PQ and PR are produced to A and B respectively. The bisectors of $\angle {AQR}$ and $\angle {BRQ}$ intersect at point O. If $\angle {QOR} = 50^{\circ}$ what is the value of $\angle {QPR}$ ?

Option 1: $50^{\circ}$

Option 2: $60^{\circ}$

Option 3: $80^{\circ}$

Option 4: $100^{\circ}$

Question : $PQR$ is a triangle, whose area is 180 cm². $S$ is a point on side $QR$ such that $PS$ is the angle bisector of $\angle QPR$. If $PQ: PR = 2:3$, then what is the area (in cm²) of triangle $PSR$?

Option 1: 90

Option 2: 108

Option 3: 144

Option 4: 72