1. In the following figure, lines AB and CD
intersect at O. If _ AOC + Z BOE = 100° and
Z BOD = 40°; find Z BOE and reflex ⓇZ COE.
Answers
Answer:
Given:∠BOD=40
∘
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
∘
=110
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Reflex∠COE=360
∘
−110
∘
=250
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Answer:
Given: ∠AOC + ∠BOE = 70° and ∠BOD = 40°
To find: ∠BOE , and Reflex ∠COE
We know that vertically opposite angles are formed when two lines intersect and they are equal in measure. Also, sum of the adjacent angles on a straight line is equal to 180 degrees.
In Fig. 6.13, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70° and ∠BOD = 40°, find ∠BOE and reflex ∠COE.
Let ∠AOC = x and ∠BOE = y.
Then x + y = 70° ( ∠AOC + ∠BOE = 70°)
Let Reflex ∠COE = z
We can see that AB and CD are two intersecting lines, so the pair of angles formed are vertically opposite angles and they are equal.
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°.