There's a theorem for this scenario that says the average of the measures of arcs AC and BD is equal to the measure of the angle formed by the chords AB and CD. In particular,
90° = 1/2 (arc AC + arc BD)
90° = 1/2 (arc AC + 126°)
90° = 1/2 arc AC + 63°
1/2 arc AC = 27
arc AC = 54°
