4 Views

Question : Circum-centre of $\triangle PQR$ is O. If $\angle QPR=55^{\circ}$ and $\angle QRP=75^{\circ}$, What is the value (in degree) of $\angle OPR$?

Option 1: 45°

Option 2: 40°

Option 3: 65°

Option 4: 70°


Team Careers360 10th Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

Correct Answer: 40°


Solution :
In $\triangle$PQR we have,
$\angle$QPR = 55° and $\angle$QRP = 75°
⇒ $\angle$PQR = 180° – (55° + 75°) = 180° – 130° = 50°
⇒ $\angle$POR = 2 × $\angle$PQR = 2 × 50° = 100°
In $\triangle$OPR,
$\angle$OPR = $\angle$ORP [since OR = OP, both are circumradius]
⇒ $\angle$OPR + $\angle$ORP = 180° – 100° = 80°
⇒ $\angle$OPR + $\angle$OPR = 80°
⇒ 2$\angle$OPR = 80°
⇒ $\angle$OPR = 40°
Hence, the correct answer is 40°.

Know More About

Related Questions

TOEFL ® Registrations 2024
Apply
Accepted by more than 11,000 universities in over 150 countries worldwide
Manipal Online M.Com Admissions
Apply
Apply for Online M.Com from Manipal University
View All Application Forms

Upcoming Exams

Trending Articles around SSC CPO

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books