Answer:
To construct an angle of \[45{}^\circ \], steps of construction are given below: Step I: Draw a ray OA and take O as centre and with any convenient radius, draw an arc which cuts OA at P. Step II: Without disturbing the radius on the compasses, draw an arc with P as centre which cuts the first arc at Q. Step III: Again, draw an arc R with Q as centre and with same radius which intersects the arc drawn in Step 1 at P. Step IV: Take Q and R as centre and with radius more than half of length RQ. draw two arcs respectively which intersects each other at B. Step V: Join OB which intersects QR at I and produce up to C. Then, \[\angle AOC=90{}^\circ \]. Step VI: Now, take P and I as a centre and with radius more than half of length PI, draw two arcs respectively which intersect each other at D. Step VII: Join OD. Then, \[\angle AOD\]is the required angle of \[45{}^\circ \].
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