If two lines AB and OD intersect at O such that AOC 5AOD then the four angles at O are ........

Quantitative Aptitude (CDS) Coordinate Geometry

If two lines AB and OD intersect at O such that $\small \angle$ AOC = 5 $\small \angle$ AOD, then the four angles at O are

40^o, 40^o, 140^o, 140^o

30^o, 30^o, 150^o, 150^o

30^o, 45^o, 75^o, 210^o

60^o, 60^o, 120^o, 120^o

$\small \angle$ AOC = 5 $\small \angle$ AOD

$\small \angle$ AOC + $\small \angle$ AOD = 180^o

5 $\small \angle$ AOD + $\small \angle$ AOD = 180^o

$\small \angle$ AOD = 30^o = $\small \angle$ BOC ( opposite angels)

$\small \angle$ BOD = 180^o - 30^o = 150^o = $\small \angle$ AOC

Therefore four angels are = 30^o, 30^o, 150^o, 150^o

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