how can we make a  45degree angle without using protractor and without making  90degree angle and bisecting it.

Follow the given steps to construct the angle measuring 45º.

Step 1: Draw a ray AB. Draw an arc of convenient radius, while taking point A as centre. Let it intersect the ray AB at C.

Step 2: Taking C as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at D.

Step 3: Join AD. Here, ∠BAD = 60º.

Step 4: Taking C  and D as centres, draw arcs with radius more than CD. Let these arcs intersect each other at E. 

Step 5: Join AE. Here, ∠BAE = ∠DAE = 30º . Suppose AE intersects the arc CD in F.

Step 6: Taking F  and D as centres, draw arcs with radius more than FD. Let these arcs intersect each other at G. 

Step 7: Join AG. Here, ∠DAG = ∠GAE = 15º.

Here, ∠BAG = ∠BAE + ∠GAE = 30º +  15º = 45º

Thus, ∠BAG is the angle measuring 45º.