LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
25 views
in Lines and Angles by (45.2k points)
closed by

In the given figure sides QP and RQ of ∠PQR are produced to points S and T respectively. If ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.

1 Answer

+1 vote
by (44.6k points)
selected by
 
Best answer

Given that ∠SPR = 135° and ∠PQT =110°

From the figure 

∠SPR + ∠RPQ = 180° 

∠PQT + ∠PQR = 180° 

[∵ linear pair of angles] 

⇒ ∠RPQ = 180° – ∠SPR = 180° – 135° = 45° 

⇒ ∠PQR = 180° – ∠PQT = 180°-110° = 70° 

Now in APQR 

∠RPQ + ∠PQR + ∠PRQ = 180° 

[∵ angle sum property] 

∴ 45° + ’70° + ∠PRQ = 180° 

∴ ∠PRQ = 180°-115° = 65°

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...