Question

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.

Answer 1

Sum of exterior angles of hexagon formed by producing sides of order = 360°

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

50x + 10° = 360°

50x = 360° – 10°

50x = 350°

x = `350/50`

x = 7

∴ Angles are

(6x – 1)°; (10x + 2)°; (8x + 2)°; (9x – 3)°; (5x + 4)° and (12x + 6)°

i.e. (6 × 7 – 1)°, (10 × 7 + 2)°, (8 × 7 + 2)° (9 × 7 – 3)°, (5 × 7 + 4)° and (12 × 7 + 6)°

i.e. 41° ; 72°, 58° ; 60° ; 39° and 90°