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The figure shows a rectangle ABCD in which AB = x cm and BC = 2x cm. Points P and Q are on AD and CD respectively such that PD = 6 cm and DQ = 2 cm.
a) Show that the area of the shaded region is #(5x — 6) cm^2#.
b) Given that the area of triangle ABP is 40 cm2, find the value of x and hence calculate the area of the shaded region.
c) Expressing your answer in degrees and minutes use trigonometry calculate the size of the angles marked θ and β.