In Figure, lines AB and CD intersect at O. If \(∠\)AOC+\(∠\)BOE=70° and \(∠\)BOD=40°, find \(∠\)BOE and reflex \(∠\)COE.
Solution and Explanation
Given: \(∠\)AOC + \(∠\)BOE = 70° and \(∠\)BOD = 40°
To find: \(∠\) BOE, and Reflex \(∠\)COE
From Figure,
(\(∠\)AOC +\(∠\)BOE +\(∠\)COE) and (\(∠\)COE +\(∠\)BOD +\(∠\)BOE) forms a straight line.
So, \(∠\)AOC+\(∠\)BOE +\(∠\)COE = \(∠\)COE +\(∠\)BOD+\(∠\)BOE = 180°
Now, by putting the values of \(∠\)AOC + \(∠\)BOE = 70° and \(∠\)BOD = 40° we get
\(∠\)COE = 110° and \(∠\)BOE = 30°
So, reflex \(∠\)COE = 360o – 110o = 250o
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