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.