question_answer

How will you construct a \[45{}^\circ \] angle?

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 \[45{}^\circ \].