STEPS OF CONSTRUCTION
(i) Draw a ray OA.
(ii) With O as centre and a convenient radius, draw an arc, cutting OA at P.
(iii) With P as centre and the same radius as above, draw an arc, cutting the previous arc at Q.
(iv) Join OQ and produce it to a point B.
Then, `angleAOB` is the required angle of measure `60^(@)`.
Verification :
If you measure `angleAOB` by using a protractor, you will find that `angleAOB=60^(@)`.
Justification :
Join PQ, as shown in the figure.
Then, `OQ=OP=PQ` (by construction)
`:. Delta OPQ` is an equilateral triangle.
Hence, `anglePOQ=60^(@)` and therefore, `angleAOB=60^(@)`.