Question

In the given figure lines AB and LM intersect at O. If angle AOL + angle BOP = 70° and angle BOM = 40° , find angle BOP and angle AOM​

Answer 1

Answer:

SOLUTION :

∠AOC + ∠BOE = 70°

∠AOC + ∠COE + ∠BOE = 180°

[ linear pair ]

So,

if ∠AOC + ∠BOE = 70°

so,

→ 70° + ∠COE = 180°

→ ∠COE = 180 - 70

→ ∠COE = 110°

.

∠BOD = ∠AOC [ Vertically Opposite Angles ]

.

Now,

→ ∠AOC + ∠COE + ∠BOE = 180°

→ 40° + 110° + ∠BOE = 180°

→ 150° + ∠BOE = 180°

→ ∠BOE = 180° - 150°

→ ∠BOE = 30°

.

∠BOD + ∠DOA = 180° [Liner Pair]

→ 40° + ∠DOA = 180°

→ ∠DOA = 180° - 40°

→ ∠DOA = 140°

Hence,

reflex angle ( ∠COE ) = ∠AOC + ∠DOE + ∠BOD + ∠BOE

reflex angle ( ∠COE ) = 40° + 140° + 40° + 30°

reflex angle ( ∠COE ) = 250°

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