Chord AB subtracts a 125-degree arc, and chord AC subtends a 52-degree arc. Find the angle BAC.

There are two options for the location of points A, B, C on a circle.

In the first version, the chords AB and BC are located on opposite sides of the point A.

Then the degree measure of the arc BC will be equal to: BC = 360 – AB – AC = 360 – 125 – 52 = 183.

Then the angle BAC = BC / 2 = 183/2 = 91.5.

In the second case, chords AB and AC are located on the same side of point A.

Then the degree measure of the arc BC will be equal to: BC = AB – AC = 125 – 52 = 73.

Then the angle BAC = BC / 2 = 73/2 = 36.6.

Answer: The angle BAC is 91.5 or 36.5.