(a) (i) In the diagram, \(x^\circ + 90^\circ = (3x + 15)^\circ\) (Sum of opposite interior angles) Thus, \(90^\circ - 15^\circ = 3x - x \implies 75^\circ = 2x\) \(x = 37.5^\circ\) (ii) < RSQ = 90^\circ - 37.5^\circ = 52.5^\circ (b) \(2N4_{seven} = 15N_{nine}\) \(2N4_{seven} = (2 \times 7^{2}) + (N \times 7^{1}) + (4 \times 7^{0})\) = \(98 + 7N + 4\) = \(102 + 7N\) \(15N_{nine} = (1 \times 9^{2}) + (5 \times 9^{1}) + (N \times 9^{0})\) = \(81 + 45 + N\) = \(126 + N\) \(\implies 102 + 7N = 126 + N\) \(7N - N = 126 - 102 = 24\) \(6N = 24 \implies N = 4\) Therefore, \(244_{seven} = 154_{nine}\).