In Fig. 6.13 lines AB and CD intersect at O. If angle AOC+ angle BOE=70^ and angle BOD=40^ , find angle BOE and reflex angle COE
Share
In Fig. 6.13 lines AB and CD intersect at O. If angle AOC+ angle BOE=70^ and angle BOD=40^ , find angle BOE and reflex angle COE
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Answer:
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°.
Answer:
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°.
Explanation:
pls mark me as brainlist ans