Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
883 views
in Circles by (23.7k points)
closed by

O is the center of the given circle. Then ∠x + ∠y equals

(a) 2 ∠z 

(b) \(\frac{∠z }{2}\)

(c) ∠z 

(d) None of these

1 Answer

+1 vote
by (22.8k points)
selected by
 
Best answer

Answer : (c) ∠z 

∠QSR = ∠QTR = \(\frac{1}{2}\) ×∠QOR = \(\frac{z}{2}\) 

(Angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle)

∠PSM = ∠PTM = 180º - \(\frac{z}{2}\) (Straight line) 

Also, ∠SMT = ∠QMR = y (vert. opp. ∠s) 

∴ In quad. PSMT, ∠SMT + ∠PTM + ∠TPS + ∠PSM = 360° 

⇒ y + 180° – \(\frac{z}{2}\) + x + 180° – \(\frac{z}{2}\) = 360° 

x + y = z.

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

...