Steps of construction:

Step 1: A ray YZ is drawn.

Step 2: Taking Y as a centre and any random radius, draw an arc ABC cutting YZ at C.

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

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

Step 5: Now, take A and B as centre one by one, draw two arcs intersecting each other with the same radius at point X.

Step 6: X and Y are joined and a ray XY making an angle 90° with YZ is formed

Justification for construction:

We constructed ∠BYZ = 60^o

And also ∠AYB = 60^o

Thus,

∠AYZ = 120^o

Also, bisector of ∠AYB is constructed such that:

∠AYB = ∠XYA + ∠XYB

∠XYB =

∠XYB = * 60^o

∠XYB = 30^o

Now,

∠XYZ = ∠BYZ + ∠XYB

= 60^o + 30^o

= 90^o