Which of the following angles cannot be constructed using ruler and compass only ?

We can use process of elimination to find the answer.

We know that 120° = 60° + 60°

135° = 90° + 45°

37.5° is the bisected angle of 75° where 75° is the bisected angle of 90° and 60°.

Thus, 120°, 135° and 37.5° can all be constructed using ruler and compass only.

But 40° cannot be drawn using ruler and compass only.

Hence, 40° is the required angle.