Steps of construction:

Step 1: Draw a ray OA.

Step 2: With its initial point O as center and any radius, draw an arc, cutting OA at C.

Step 3: With center c and same radius (as in step 2) draw an arc cutting arc at D.

Step 4: With D as center and the same radius, draw an arc cutting the arc cutting at E.

Step 5: With D and E as centers and any convenient radius (more than DE). Draw to two arcs intersecting at P.

Step 6: Draw ∠AOB = 120° and ∠POB = 90°

Step 7: Bisect angle POB,

Then ∠AOQ is the required angle of 105°.