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Note: ∠PRS = 144° is labelled wrongly in the diagram.

(a) ∠URQ = 180° – 72° = 108° (interior angle, PQ parallel to UR)
∠a = 108° (corresponding angle, PU parallel to QR)

(b) ∠URS = ∠PQR = 72° (corresponding angle, PQ parallel to UR)
∠RUS = 180° – 72° – 46° = 62° (sum of angles in triangle)
∠SUT = 180° – 62° = 118° (sum of angles on straight line)
∠b = ∠UST (△UTS is isosceles triangle)
∠b = (180° – 118°)/2 = 31° (sum of angles in triangle)

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(a) ∠PUR  = ∠PQR =  72º   Opposite angle of parallelogram equals

∠a = 180º – 72º = 108º

(b)  ∠URS = ∠PUR = 72º                 Alternate angle of Parallelogram equals

∠SUT = 72º + 46º = 118º                 Sum of opposite  interior angles of triangle equal exterior angle

∠b = (180º – 118º)/2 = 31º                triangle SUT isosceles.

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