The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are $(6 x - 1)^{o}, (10 x + 2)^{o}, (8 x + 2)^{o} (9 x - 3)^{o}, (5 x + 4)^{o} a n d (12 x + 6)^{o}$ ; find each exterior angle.

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Solution

Sum of exterior angles of hexagon formed by producing sides of order = $360^{o}$

$∴ (6 x - 1)^{o} + (10 x + 2)^{o} + (8 x + 2)^{o} + (9 x - 3)^{o} + (5 x + 4)^{o} + (12 x + 6)^{o} = 360^{o} 50 x + 10^{o} = 360^{o} 50 x = 360^{o} - 10^{o} 50 x = 350^{o} x = \frac{350}{50} x = 7 ∴ A n g l e s a r e (6 x - 1)^{o}; (10 x + 2)^{o}; (8 x + 2)^{o}; (9 x - 3)^{o}; (5 x + 4)^{o} a n d (12 x + 6)^{o} i . e ., (6 \times 7 - 1)^{o}; (10 \times 7 + 2)^{o}; (8 \times 7 + 2)^{o}; (9 \times 7 - 3)^{o}; (5 \times 7 + 4)^{o}; (12 \times 7 + 6)^{o} i . e . 41^{o}; 72^{o}, 58^{o}; 60^{o}; 39^{o} a n d 90^{o}$ .

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