Steps of construction:

Step 1: Draw an angle AOB = 90°

Step 2: Draw the bisector OC of ∠AOB, then ∠AOC = 45°

Step 3:Bisect ∠AOC, such that ∠AOD = ∠COD = 22.5°

Thus ∠AOD = 22.5°

Verification:

On measuring ∠AOD, with the protractor,

we find ∠ AOD = 22.5° .