The chord MN contracts the arc equal to 123 degrees and the chord MN contracts the arc by 51 degrees find the angle HMN.

There are two options for the location of points M, N, H on a circle.

In the first version, the chords MH and MN are located on opposite sides of the point M.

Then the degree measure of the arc NH will be: NH = 360 – MH – MN = 360 – 123 – 51 = 186.

Then the angle HMN = NH / 2 = 186/2 = 93.

In the second case, the chords MH and MN are located on the same side of the point M.

Then the degree measure of the arc NH will be: NH = MH – MN = 123 – 51 = 72.

Then the angle is HMN = NH / 2 = 72/2 = 36.

Answer: The BAC angle is 93 or 36.