Construct an angle of `60^(@)` using ruler and compasses only Justify your construction.

Explanation

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^(@)`.