The deployed ABC is divided by the BE beam into two angles with a ratio of 4: 6. Find the angle between

The deployed ABC is divided by the BE beam into two angles with a ratio of 4: 6. Find the angle between the beam BE and the bisector ∠ABС.

The flattened angle is 180 degrees. Beam BE divides the unfolded angle into angles, in a ratio of 4/6.

Then 180 = 6 * X + 4 * X = 10 * X.

X = 180/10 = 18.

Angle ABE = 18 * 6 = 108.

EBC angle = 18 * 4 = 72.

Since the ВK beam is the bisector of the unfolded angle, then it is perpendicular to the AC, then the angle KBC = KВA = 90.

Then the angle KBE = 90 – EBC = 90 – 72 = 18.

Or KBE = ABE – 90 = 108 – 90 = 18.

Answer: Angle ABE = 18.