For which acute angles is the following statement true? The complement of the angle is smaller in measure than either of the two angles into which the bisector divides the acute angle

Let the acute angle be 2x.

Its complement is 90 - 2x.

It is given that this complementary angle is less than each of the bisected angle.

Therefore, 90 - 2x < x

90 < 3x

or, x > 30.

2x > 60

Therefore, the statement is true for all angles that are greater than 60 degrees.