Steps of construction:

Step 1: Draw a ray OY.

Step 2: Taking O as a centre and any radius, mark a point C on the arc ABC.

Step3: Taking A as a centre and the same radius, mark a point B on the arc ABC.

Step 4: Taking B as a centre and the same radius, mark a point C on the arc ABC.

Step 5: Now, take A and B as centre one by one, draw an arc from each center intersecting each other at a point X.

Step 6: X and Y are joined and a ray making an angle with YZ is formed.

Step 7: With A and E as centres, 2 arcs are marked intersecting each other at D and the bisector of angle XOY is drawn.

The justification for construction:

By construction,

∠XOY= 90⁰

We constructed the bisector of ∠XOY as ∠DOY

Thus,

∠DOY= ½ ∠XOY = ½ 90⁰ = 45⁰