AB and CD are two chords of a circle which intersect at E inside the circle. If ∠BEC = 125° and ∠EBD = 28°, then what is the measure of ∠BAC ?

97°

As, CD is a straight line.

So, ∠BEC + ∠BED = 180º

125º + ∠BED = 180º

∠BED= 55º

In triangle BED,

∠B + ∠E + ∠D = 180º

28º + 55º + ∠D = 180º

∠D = 97º

Property we going to use here is :- Angles made by same segment on circumference are equal. 

⇒  ∠D = ∠A

So, ∠A  = 97º

Hence , ∠BAC  = 97º