(a) 
In the diagram
(i) The value of x; (ii)
(b) If \(2N4_{seven} = 15N_{nine}\), find the value of N.
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, \(244_{seven} = 154_{nine}\).