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Question

The sides of a hexagon are produced in order. If the measures of exterior angles so obtained are (6x1)o, (10x+2)o, (8x+2)o (9x3)o, (5x+4)o and (12x+6)o; find each exterior angle.


Solution

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

(6x1)o+(10x+2)o+(8x+2)o+(9x3)o+(5x+4)o+(12x+6)o=360o50x+10o=360o50x=360o10o50x=350ox=35050x=7Angles are(6x1)o; (10x+2)o;(8x+2)o; (9x3)o; (5x+4)o and (12x+6)oi.e.,(6×71)o; (10×7+2)o; (8×7+2)o; (9×73)o; (5×7+4)o; (12×7+6)oi.e. 41o; 72o,58o; 60o;39o and 90o.

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