In the adjoining figure lines AB and CD intersect at O angle AOD :AOC =1:2.then find Angle BOD and BOC
Answers
Answer:
25°
Step-by-step explanation:
Given:∠BOD=40
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Since AB and CD intersects, ∠AOC=∠BOD(vertically opposite angles)
∠AOC=40
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Also,∠AOC+∠BOE=70
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⇒∠BOE=70
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−∠AOC=70
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−40
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=30
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We need to find reflex∠COE
Reflex∠COE=360
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−∠COE
Now, ∠AOC+∠COE+∠BOE=180
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⇒∠COE+(∠AOC+∠BOE)=180
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⇒∠COE+(40
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+30
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)=180
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⇒∠COE=180
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−70
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=110
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Reflex∠COE=360
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−110
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=250
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Question :-
In figure, lines AB and CD intersect at 0. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
Answer :-
Since AB is a straight line,
∴ ∠AOC + ∠COE + ∠EOB = 180°
o r (∠AOC + ∠BOE) + ∠COE = 180° or 70° + ∠COE = 180° [ ∵∠AOC + ∠BOE = 70° (Given)]
or ∠COE = 180° – 70° = 110°
∴ Reflex ∠COE = 360° – 110° = 250°
Also, AB and CD intersect at O.
∴∠COA = ∠BOD [Vertically opposite angles]
But ∠BOD = 40° [Given]
∴ ∠COA = 40°
Also, ∠AOC + ∠BOE = 70°
∴ 40° + ∠BOE = 70° or ∠BOE = 70° -40° = 30°
Thus, ∠BOE = 30° and reflex ∠COE = 250°.
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