Question
Download Solution PDFABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
∠BEC = 138° and ∠ECD = 35°
Concept used:
In cyclic quadrilateral angles on the same arc are always same
Calculation:
∠BEC and ∠CED are on the same straight lines
∠BEC =138°
∠CED = 180° – 138°
⇒ ∠CED = 42°
In ΔCDE, ∠CED = 42° and ∠DCE = 35°
∠CDE = 180° - (42° + 35°)
∠CDE = 103°
∠BAC and ∠BDC are on the same arc BC
We know that In cyclic quadrilateral angles on the same arc are always same.
∠BAC = 103°
∴ The measure of ∠BAC is 103°
Last updated on Jun 2, 2025
-> The SSC Exam Dates 2025 has been released on the official website.
-> The SSC CGL Notification 2025 will be released on 9th June 2025 at ssc.gov.in.
-> The SSC CGL application 2025 submission will be open from 9th June to 4th July 2025.
-> The SSC CGL Tier 1 Exam 2025 Dates have been revised. The SSC CGL Exam will be conducted from 13 August to 30 August, 2025.
-> Candidates can refer to the SSC CGL syllabus for a better understanding of the exam structure and pattern.
-> The SSC CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.
-> Candidates should also use the SSC CGL previous year papers for a good revision.