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In Fig. 6.13, lines AB and CD intersect at O. If ∠ AOC + ∠ BOE = 70° and ∠ BOD = 40°, find ∠ BOE and reflex ∠ COE.

1. In Fig. 6.13, lines AB and CD intersect at O. If \angle AOC + \angle BOE = 70° and \angle BOD = 40°, find \angleBOE and reflex \angleCOE.

                        

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Given that,
AB is a straight line. Lines AB and CD intersect at O. \angle AOC + \angle BOE = 70^0 and \angle BOD = 40^0
Since AB is a straight line
\therefore \angleAOC + \angleCOE + \angleEOB = 180^0
\Rightarrow \angle COE = 180^0-70^0=110^0 [since \angle AOC + \angle BOE = 70^0]

So, reflex \angleCOE = 360^0-110^0 = 250^0
It is given that AB and CD intersect at O
Therefore, \angleAOC  = \angleBOD  [vertically opposite angle]
\Rightarrow \angle COA = 40^0 [ GIven \angle BOD = 40^0]
Also, \angle AOC + \angle BOE = 70^0
So,  \angleBOE = 30^0

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