1 View

Question : In $\triangle$PQR, the angle bisector of $\angle$P intersects QR at M. If PQ = PR, then what is the value of $\angle$PMQ?

Option 1: 75°

Option 2: 80°

Option 3: 70°

Option 4: 90°


Team Careers360 25th Jan, 2024
Answer (1)
Team Careers360 26th Jan, 2024

Correct Answer: 90°


Solution :
In $\triangle$PQR, PQ = PR
⇒ $\angle$Q = $\angle$R = b
PM is the angle bisector of $\angle$P.
$\angle$QPM = $\angle$RPM = a
Apply angle sum property in $\triangle$PQR,
⇒ $\angle$P + $\angle$Q + $\angle$R = 180°
⇒ $\angle$P + b + b = 180°
⇒ $\angle$P = 180° – 2b
$\angle$QPM = $\frac{180° – 2b}{2}$ = 90° – b
In $\triangle$PQM,
Let $\angle$PMQ = $\theta$
⇒ $\angle$QPM + $\angle$Q + $\angle$M = 180°
⇒ 90° – b + b + $\theta$ = 180°
⇒ $\theta$ = 90°
Hence, the correct answer is 90°.

How to crack SSC CHSL

Candidates can download this e-book to give a boost to thier preparation.

Download Now

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
GRE ® Registrations 2024
Apply
Apply for GRE® Test now & save 10% with ApplyShop Gift Card | World's most used Admission Test for Graduate & Professional Schools
View All Application Forms

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