Draw a right angle and construct its bisector.

Steps:

1. Draw any line l and take a point O on it.

2. With O as centre and suitable radius, draw an arc to cut the line l at points A and B.

3. With A and B as centres, draw two arcs of equal radius $\left(\gt\dfrac{1}{2}\text{AB}\right)$ cutting each other at C.

4. Join OC and produce it to form ray OC. Then ∠BOC = 90°.

5. To bisect ∠BOC, with O as centre and any suitable radius, draw an arc to meet OB at P and OC at Q.

6. With P and Q as centres and equal radii $\left(\gt\dfrac{1}{2}\text{PQ}\right)$, draw two arcs cutting each other at D.

7. Join OD and produce it to form a ray.

Hence, ray OD is the bisector of right angle ∠BOC, and ∠BOD = ∠DOC = 45°.