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°
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