0 votes
in Circle by (45.5k points)
closed by

An exterior angle of a cyclic quadrilateral is congruent to the angle opposite to its adjacent interior angle

Given: ABCD is a cyclic quadrilateral. 

∠BCE is the exterior angle of ABCD. 

To prove: ∠BCE ≅ ∠BAD

1 Answer

+1 vote
by (47.5k points)
selected by
Best answer


∠BCE + ∠BCD = 180°…… (i) [Angles in a linear pair] 

⟂ABCD is a cyclic quadrilateral. [Given] 

∠BAD + ∠BCD = 180°………. (ii) [Opposite angles of a cyclic quadrilateral are supplementary] 

∴ ∠BCE + ∠BCD = ∠BAD + ∠BCD [From (i) and (ii)] 

∴ ∠BCE = ∠B

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.