Question : In $\triangle \mathrm{PQR}, \angle \mathrm{P}=46^{\circ}$ and $\angle \mathrm{R}=64^{\circ}$.If $\triangle \mathrm{PQR}$ is similar to $\triangle \mathrm{ABC}$ and in correspondence, then what is the value of $\angle \mathrm{B}$?
Option 1: 70°
Option 2: 90°
Option 3: 100°
Option 4: 110°
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 70°
Solution : $\angle$P = 46$^{\circ}$ $\angle$R = 64$^{\circ}$ In correspondence with $\triangle$PQR, we have $\triangle$ABC. Let's denote the corresponding angles of $\triangle$ABC as $\angle$A, $\angle$B, and $\angle$C. According to the property of similar triangles, the corresponding angles of similar triangles are equal. So, $\angle$P = $\angle$A $\angle$Q = $\angle$B $\angle$R = $\angle$C Using the given angle measures, we have: $\angle$P = $\angle$A = 46$^{\circ}$ $\angle$Q = $\angle$B $\angle$R = $\angle$C = 64$^{\circ}$ $\because$ The sum of angles in a triangle is 180°, $\angle$Q = 180$^{\circ}$ - $\angle$P - $\angle$R $\angle$Q = 180$^{\circ}$ - 46$^{\circ}$ - 64$^{\circ}$ $\angle$Q = 70$^{\circ}$ $\therefore$ The value of $\angle$B is 70$^{\circ}$ Hence, the correct answer is 70$^{\circ}$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
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?
Question : In a triangle $\triangle \mathrm{PQR}$, the bisectors of $\angle \mathrm{P}$ and $\angle \mathrm{R}$ meet at a point $\mathrm{M}$ inside the triangle. If the measurement of $\angle P M R=127^{\circ}$, then the measurement of $\angle Q$ is:
Question : $O$ is the orthocentre of triangle $ABC$, and if $\angle BOC = 110^\circ$, then $\angle BAC$ will be:
Question : It is given that $\triangle \mathrm{PQR} \cong \triangle \mathrm{MNY}$ and $PQ=8\ \mathrm{cm}, \angle Q = 55°$ and $\angle P = 72°$. Which of the following is true?
Question : In $\triangle \mathrm{ABC}, \angle \mathrm{A}=5 \mathrm{x}-60^{\circ}, \angle \mathrm{B}=2 \mathrm{x}+40^{\circ}, \angle \mathrm{C}=3 \mathrm{x}-80^{\circ}$. Find $\angle \mathrm{A}$.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile