Area of a sector = $\;{θ}/{360}$ x $π$ r$^2$
51.3 = $\;{θ}/{360}$ x $\;{22}/{7}$ x 7 x 7
$θ$ = $\;{51.3 × 360}/{22 × 7}$ = 119.9 ≈ 120º to the nearest whole number.
