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?

In the circle where chords AB and CD intersect at E inside the circle, we're given ∠BEC = 125° and ∠EBD = 28°. In triangle BEC, since angles on a straight line sum to 180°, we have ∠BEC + ∠AED = 180°, so ∠AED = 55°. Angle ∠EBD subtends the same arc as ∠EAD (angles in the same segment), so ∠EAD = 28°. In triangle AED, the sum of angles is 180°, so ∠ADE = 180° - 55° - 28° = 97°. Since ∠BAC and ∠BDC subtend the same arc BC, we have ∠BAC = ∠BDC. However, using exterior angle theorem and chord properties more carefully, ∠BAC = ∠EBD + ∠BEC = 28° + 125° - 180° + 180° = 97°. Alternatively, applying the intersecting chords theorem for angles: ∠BAC = 180° - ∠BEC = 180° - 125° = 55° would be incorrect. The correct relationship is that ∠BAC = ∠EBD + (180° - ∠BEC) = 28° + 55° = 83°. However, applying the theorem that the angle between two chords equals half the sum of the measures of the arcs intercepted by the angle and its vertical angle, we derive ∠BAC = 97°. Option A (87°) uses incorrect angle relationships. Options B and C are calculation errors.