1.

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

Answer»

Solution :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^(@)`.


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