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Is given an angle £ and an segment AB. Haw can I draw an arc from A to B such the central angle corresponding to it to be £ ?

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If you find any point $C$ such that $\angle ACB = £/2$, then the $AB$ arc of the circumcircle of $\triangle ABC$ will work.

You can do this by finding any two angles that add to $180^\circ - £/2$, and drawing one of them at $A$ and the other one at $B$, both with $AB$ as one of the angle legs, and let $C$ be where the two new angle legs intersect.

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