calculate angle AOC angle BOD and angle AOE in the adjoining figure it is being given that angle COD equal 90 degree angle BOE = 72 degree and angle AOB is a straight line
Answers
ANSWER :-
Since AB is line ,
3x + 72 = 180°
3x = 180 - 72
3x = 108
∴ x = 36
∠OAC = x = 36°
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90+y+72+3x+x = 360
162 + y + 4x = 360
y + 4(36) = 198
y + 144 = 198
∴ y = 54
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∠BOD = y = 54°
∠AOE = 3x = 3(36)
∠AOE = 108°
★Calculate ∠AOC, ∠BOD and ∠AOE in the adjoining figure, it is being given that ∠COD = 90°, ∠BOE = 72° and ∠AOB is a straight line.
Since, AOB is a straight line the sum of all angles on the lower side of AOB at the point O on it, is 180°.
∴ ∠AOB + ∠BOE = 180°
==> 3x + 72° = 180°
==> 3x = (180° – 72°)
==> 3x = 108°
==> x = 108/3
==> x = 36°
Again, AOB is a straight line and O is a point on it.
So, the sum of all angles on the upper side of AOB at a point O on it,is 180°.
∴ ∠AOC + ∠COD + ∠DOB = 180°
==> x + 90 + y = 180 [∵ ∠AOC = x°, ∠COD = 90° and ∠DOB = y°]
==> 36 + 90 + y = 180 [∵ x = 36°]
==> 126° + y° = 180°
==> y = 180 – 126
==> y = 54°
∴ ∠AOC = x° = 36°, ∠BOD = y° = 54°
∠AOC = 3x = (36 × 3) = 108°