The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x - 1)°, (10x + 2)°, (8x+ 2)°, (9x - 3)°, (5x + 4)° and (12x + 6)°, find each exterior angle.

According to the property of polygons, the sum of all exterior angles of a polygon is always 360°.

So,

(6x - 1)° + (10x + 2)° + (8x + 2)° + (9x - 3)° + (5x + 4)° + (12x + 6)° = 360°

⇒ 6x° - 1° + 10x° + 2° + 8x° + 2° + 9x° - 3° + 5x° + 4° + 12x° + 6° = 360°

⇒ 50x° + 10° = 360°

⇒ 50x° = 360° - 10°

⇒ 50x° = 350°

⇒ x° = $\dfrac{350°}{50°}$

⇒ x = 7°

So, the exterior angles are calculated as follows:

(6x - 1)° = (6 $\times$ 7 - 1)° = (42 - 1)° = 41°

(10x + 2)° = (10 $\times$ 7 + 2)° = (70 + 2)° = 72°

(8x + 2)° = (8 $\times$ 7 + 2)° = (56 + 2)° = 58°

(9x - 3)° = (9 $\times$ 7 - 3)° = (63 - 3)° = 60°

(5x + 4)° = (5 $\times$ 7 + 4)° = (35 + 4)° = 39°

(12x + 6)° = (12 $\times$ 7 + 6)° = (84 + 6)° = 90°

Hence, the exterior angles are 41°, 72°, 58°, 60°, 39° and 90°.