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

I case. Point C does not belong to arc AB.

The whole circle is equal to the sum of the arcs AB, AC and BC. The whole circle is 360 °.

Hence, the arc BC = 360 ° – (AB + AC) = 360 ° – (125 ° + 52 °) = 360 ° – 177 ° = 183 °.

The inscribed angle is equal to half of the arc on which it rests. The BAC angle rests on the BC arc, therefore, the BAC angle is 183 °: 2 = 92.5 °.

Answer: angle BAC = 92.5 °.

II case. Point C belongs to arc AB.

Then the arc BC is equal to the difference between the arcs AB and AC:

BC = AB – AC = 125 ° – 52 ° = 73 °.

The inscribed angle is equal to half of the arc on which it rests. The BAC angle rests on the BC arc, therefore, the BAC angle is 73 °: 2 = 36.5 °.

Answer: angle BAC = 36.5 °.