In Fig. 8.62, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40° find ∠BOE and reflex ∠COE.
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Answered by
14
∠BOE = 30° and reflex∠COE = 110°
Explanation:
Given data:
AB and CD are intersecting lines.
∠AOC + ∠BOE = 70° and ∠BOD = 40°
Sum of angle in linear pair = 180°
⇒ ∠COE = 110°
Sum of angle in linear pair = 180°
⇒ ∠BOE = 30°
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In fig 6.13 lines AB and CD intersect at O.if Angle AOC+AngleBOE =70° and Angle BOD =40° ,find ANGLE BOE and Reflex Angle COE.
https://brainly.in/question/3121202
Answered by
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In figure, lines AB and CD intersect at 0. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE
Since AB is a straight line,
- ∠AOC + ∠COE + ∠EOB = 180°
- or (∠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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