In a right-angled triangle with a right angle C, the bisector BE is drawn, find the angle BAC if the angle BEA = 115.

The angle BEA and BEC are adjacent angles, the sum of which is 180, then the angle BEC = (180 – BEA) = (180 – 115) = 65.

In a triangle BCE, the angle BCE = 90, and the angle BEC = 65, then the angle CBE = (180 – 90 – 65) = 25.

Since BE is the bisector of angle B, the angle ABE = BEC = 25, and then the angle ABC = 2 * 25 = 50.

Angle BAC = (180 – ACB – ABC) = (180 – 90 – 50) = 40.

Answer: Angle BAC = 40.