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$^{\circ}$
Latest: SSC CGL Tier 1 Result 2024 Out | SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL Tier 1 Scorecard 2024 Released | SSC CGL complete guide
Suggested: Month-wise Current Affairs | Upcoming Government Exams
Correct Answer: 64$^{\circ}$
Solution :
$\angle Q P S=\frac{1}{2} \angle P S R$ Let $\angle PSR = 2\theta$ and $\angle QPS = \theta$ Sum of all the sides of the triangle = $180^{\circ}$ ⇒ $\angle QPR + \angle PRS + \angle RQP = 180^{\circ}$ ⇒ $78^{\circ} + 44^{\circ} + \angle RQP = 180^{\circ}$ ⇒ $122^{\circ} + \angle RQP = 180^{\circ}$ ⇒ $ \angle RQP = 180^{\circ}- 122^{\circ} = 58^{\circ}$ $\angle PSR$ = exterior angle of $\angle PSQ$ ⇒ $2\theta = \theta + 58^{\circ}$ ⇒ $2\theta - \theta = 58^{\circ}$ ⇒ $\theta = 58^{\circ}$ $\angle PSQ = 180^{\circ} - 2\theta$ $= 180^{\circ} - 2×58^{\circ}$ $= 180^{\circ} - 116^{\circ}$ $= 64^{\circ}$ Hence, the correct answer is 64$^{\circ}$.
Candidates can download this ebook to know all about SSC CGL.
Result | Eligibility | Application | Selection Process | Preparation Tips | Admit Card | Answer Key
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 $\angle {PSR}$?
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 a triangle ${ABC}, {D}$ is a point on ${BC}$ such that $\frac{A B}{A C}=\frac{B D}{D C}$. If $\angle B=68^{\circ}$ and $\angle C=52^{\circ}$, then measure of $\angle B A D$ is equal to:
Question : In $\triangle {ABC}$, D is a point on BC such that $\angle {ADB}=2 \angle {DAC}, \angle {BAC}=70^{\circ}$ and $\angle {B}=56^{\circ}$. What is the measure of $\angle A D C$?
Question : In $\triangle P Q R$, $\angle Q=90^{\circ}$, $PQ=8$ cm and $\angle P R Q=45^{\circ}$ Find the length of $QR$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile