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Lines AB and CD intersect at O. If Angle AOC + Angle BOE = 70 and BOD = 40 find Angle BOE and reflex Angle COE subject maths


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Answer 1

Step-by-step explanation:

Solution:-

Given: ∠AOC + ∠BOE = 70° and ∠BOD = 40°

⚜

⚜To find: ∠BOE , and Reflex ∠COE

⚜Let ∠AOC = x and ∠BOE = y.

⚜Then x + y = 70° ( ∠AOC + ∠BOE = 70°)

⚜Let Reflex ∠COE = z

i.e, ∠AOD = ∠BOC and ∠AOC = ∠BOD.

Since ∠AOC = x and ∠AOC = ∠BOD = 40°

⚜Thus, we can say that x = 40°.

⚜Also we know that,

x + y = 70°

40° + y = 70°

y = 70° - 40° = 30°

∠BOE = 30°

⚜If we consider line AB and ray OD on it, then ∠AOD and ∠BOD are adjacent angles.

∠AOD + ∠BOD = 180°

∠AOD + 40° = 180°

∠AOD = 180° - 40°

= 140°

⚜Reflex ∠COE = ∠AOC + ∠AOD + ∠BOD + ∠BOE

= 40° + 140° + 40° + 30°

= 250°

Thus, ∠BOE = 30° and the reflex ∠COE = 250°.

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Answer 2

Step-by-step explanation:

Solution:-

Given: ∠AOC + ∠BOE = 70° and ∠BOD = 40°

To find: ∠BOE , and Reflex ∠COE

Let ∠AOC = x and ∠BOE = y.

lThen x + y = 70° ( ∠AOC + ∠BOE = 70°)

Let Reflex ∠COE = z

i.e, ∠AOD = ∠BOC and ∠AOC = ∠BOD.

Since ∠AOC = x and ∠AOC = ∠BOD = 40°

Thus, we can say that x = 40°.

Also we know that,

x + y = 70°

40° + y = 70°

y = 70° - 40° = 30°

∠BOE = 30°

If we consider line AB and ray OD on it, then ∠AOD and ∠BOD are adjacent angles.

∠AOD + ∠BOD = 180°

∠AOD + 40° = 180°

∠AOD = 180° - 40°

= 140°

Reflex ∠COE = ∠AOC + ∠AOD + ∠BOD + ∠BOE

= 40° + 140° + 40° + 30°

= 250°

Thus, ∠BOE = 30° and the reflex ∠COE = 250°.