calculate angle AOC angle BOD and angle AOE in the adjoining figure it

1.	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
Answer» $\bf\underline{\underline{\pink{Question:-}}}$ ★Calculate ∠AOC, ∠BOD and ∠AOE in the adjoining figure, it is being given that ∠COD = 90°, ∠BOE = 72° and ∠AOB is a straight LINE. $\bf\underline{\underline{\blue{Solution:-}}}$ 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°

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

Answer»

$\bf\underline{\underline{\pink{Question:-}}}$

★Calculate ∠AOC, ∠BOD and ∠AOE in the adjoining figure, it is being given that ∠COD = 90°, ∠BOE = 72° and ∠AOB is a straight LINE.

$\bf\underline{\underline{\blue{Solution:-}}}$

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°