(a) In the diagram (i) The value of x; (ii) (b) If \(2N4_{seven} = 15N_{nine}\),...

Explanation

(a)

(i) In the diagram,

\(x° + 90° = (3x + 15)°\) (Sum of opposite interior angles)

Thus, \(90° - 15° = 3x - x \implies 75° = 2x\)

\(x = 37.5°\)

(ii)

< RSQ = 90° - 37.5° = 52.5°

(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, \(244_{seven} = 154_{nine}\).