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In order to derive the formula to calculate the angle at the centre of the sector, the formulae for the arc length and area of a sector can be rearranged so that we can calculate the fraction of \(360^\circ\).

\(Angle = \frac{{Arc\,length}}{{\pi d}} \times 360^\circ\)

\(Angle = \frac{{Area\,of\,sector}}{{\pi {r^2}}} \times 360^\circ\)

\(\frac{{Angle}}{{360^\circ }} = \frac{{Arc\,length}}{{\pi d}} = \frac{{Area\,of\,sector}}{{\pi {r^2}}}\)

\(Angle = \frac{{Arc\,length}}{{\pi d}} \times 360^\circ\)

\(Angle = \frac{3}{{\pi \times 20}} \times 360^\circ\)

\(=\frac{3}{62.8}\times 360^\circ\)

\(Angle = 17^\circ\) (to the nearest degree)