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 : 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 : In a cyclic quadrilateral ABCD, the side AB is extended to a point X. If $\angle XBC=82°$ and $\angle ADB=47°$, then the value of $\angle BDC$ is:

Option 1: 40°

Option 2: 35°

Option 3: 30°

Option 4: 25°

Question : If $ABC \cong PQR$ and $\angle ABC = (x + 60)°$, $\angle PQR = (85 – 4x)°$, and $\angle RPQ = (3x + 65)°,$ then the value of $\angle ABC$ in degree is:

Option 1: 15°

Option 2: 5°

Option 3: 45°

Option 4: 65°

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