Question

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 1

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

★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°

Answer 2

Given: The angle COD equal 90 degree angle BOE = 72 degree and angle AOB is a straight line​.

To find: The angle AOC, angle BOD and angle AOE.

Solution:

As given in the question, ∠AOB is a straight line and hence, is equal to 180°. So, the angles 72° and 3x° add up to give 180°. The angles 90°, x° and y° also add up to give 180°. These equations can be represented as follows.

$3x + 72 = 180$

$x = 36$

Now, the value of 3x is found to be,

$3x = 108$

$90 + x + y= 180$

$90 + 36 + y = 180$

$y = 54$

Hence, the value of y is found to be 54°.

Therefore, ∠AOC is 36°, ∠BOD is 54° and ∠AOE is 108°.