Option (A):

37.5° = 1/2 × 75°

75° can be constructed with the help of a ruler and a compass.

Option (B):

40° = 1/2 × 20°

This is not possible.

20° cannot be constructed with the help of a ruler and a compass.

Option (C):

22.5° = 1/2 × 45°

45° can be constructed with the help of a ruler and a compass.

Option (D):

67.5° = 1/2 × 135° = 1/2 × (90° + 45°)

Both 90° and 45° can be constructed with the help of a ruler and a compass.

Ans. (B) It is not possible to construct an angle of 40° with the help of ruler and compass.