Chord AB subtends an arc equal to 119 degrees, and chord AC-arc equal to 43 degrees. 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 – 119 – 43 = 198.

Then the angle BAC = BC / 2 = 198/2 = 99.

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

Then the degree measure of the arc BC will be equal to: BC = AB – AC = 119 – 43 = 76.

Then the angle BAC = BC / 2 = 76/2 = 38.

Answer: The BAC angle is 99 or 38.