(a)(i) ∠PSQ = ∠QPS ∠PQS = \(\frac{2}{8}\) x 180^\circ =45^\circ ∠SPQ = ∠PSQ = \(\frac{3}{8}\) x 180 = 67.5^\circ ∠SQR = ∠SPR= 26^\circ ∠PQR = ∠PQS + ∠SQR = 45^\circ+ 26^\circ = 71^\circ (ii) ∠RPQ = ∠SPQ - ∠SPR = 67.5^\circ- 26^\circ = 41.5^\circ (iii) ∠PRQ = 180^\circ - 41.5^\circ - 71^\circ = 67.5^\circ (b) |PQ| = \(\sqrt{ (x_2 - x_1)^2 + (y_2 - y_1)^2}\) 29 = \(\sqrt{ (5 - 7)^2 + (x - 3)^2}\) Take the square of both sides \(29^2\) = \(-2)^2 + (x - 3)^2 841 = 4 + x\(^2\) - 6x + 9 841 = x\(^2\) - 6x + 13 0 = x\(^2\) - 6x + 13 - 841 x\(^2\) - 6x - 828 = 0 Using the formula method where a = 1, b = -6, and c = -828 x = 31.93095 or - 25.93095 Therefore x ≈ 31. 93 or x = - 25.93