On bisecting 45°, we get

Steps of Construction

1. Draw a line segment OA.

2. At A, draw ∠AOE=90° , using ruler and compass.

3. With B as centre and radius more than half of BD, draw an arc.

4. With D as centre and same radius draw another arc which cuts the previous arc at F.

5. Join OF. ∠AOF=45°

6. Now with centre B and radius more than half of BC, draw an arc.

7. With centre C and same radius draw another arc which cuts the previously drawn arc at X.

8. Join OX

Therefore, OX is the bisector of ∠AOF.