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°
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 54°
Solution : Let $\angle QPS$ be $\theta$ ⇒ $\angle PSQ = 96^\circ + \theta$ Now, In $\triangle PQR$ ⇒ $\angle Q + \angle R = 180^\circ - \angle P$ $= 180^\circ -132^\circ$ $=48^\circ$ Since $PQ = PR$ $\angle Q = \angle R$ $\therefore \angle Q = \angle R = 24^\circ$ Now, In $\triangle PQS$ $(96^\circ + \theta ) + \theta + 24^\circ = 180^\circ$ ⇒ $2\theta = 60^\circ$ ⇒ $\theta = 30^\circ$ ⇒ $\angle PSQ = 96^\circ + 30^\circ = 126^\circ $ $\therefore \angle PSR = 180^\circ - 126^\circ=54^\circ$ Hence, the correct answer is $54^\circ$.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
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 = ?
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 $\angle \mathrm{PSQ}$.
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 $\angle PSQ$?
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 $\angle {QPR}$ ?
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 $PSR$?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile