The MK chord subtends an arc equal to 118 degrees, and the MB chord subtends

The MK chord subtends an arc equal to 118 degrees, and the MB chord subtends an arc of 54 degrees. Find the BMK angle.

There are two options for the location of points M, K, B on a circle.

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

Then the degree measure of the arc BK will be equal to: BK = 360 – MK – MB = 360 – 118 – 54 = 188.

Then the angle BMK = BK / 2 = 188/2 = 940.

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

Then the degree measure of the arc BK will be equal to: BK = MK – MB = 118 – 54 = 64.

Then the angle BMC = BK / 2 = 64/2 = 32.

Answer: The BAC angle is 94 or 32.