ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 128º and ∠ECD = 25º, then what is the measure of ∠BAC?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 103º
Concept
Angle made by the same arc on the perimeter is same.
Application
ABCD is a cyclic quadrilateral.
∠ECD = 25º (Given)
Therefore, ∠DBA = 25º (Angle made by same arc on perimeter is same)
∠BEC + ∠AEB = 180º (Straight line)
128º + ∠AEB = 180º
∠AEB = 52º
In triangle AEB
∠DBA + ∠AEB + ∠BAC = 180º
Putting the values
25º + 52º + ∠BAC = 180º
∠BAC = 103º