Question

please give answer for this question​

Answer 1

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Angle AOC = 45°

Angle BOD = 45°

Angle AOE = 135°

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Answer 2

Answer :

• ∠AOC = 45°
• ∠AOE = 135°
• ∠BOD = 78°

Step-by-step explanation :

To Find,

• The measure of ∠AOC , ∠BOD and ∠AOE

Solution,

Given that,

• ∠AOC = x°
• ∠AOE = 3x°
• ∠COD = 90°
• ∠BOD = y°
• ∠BOE = 12°

The measure of ∠AOC and ∠AOE is

» ∠AOC + ∠AOE = EOC ( 180° ) ..... supplementary angle

» x + 3x = 180

» 4x = 180

» x = 180 / 4

» x = 90 / 2

» x = 45

Therefore, the angles are :-

• ∠AOC = x ➯ 45°
• ∠AOE = 3x ➯ 3 × 45 ➯ 135°

The measure of ∠BOD is

» ∠COD + ∠BOD + ∠BOE = COE ( 180° ) ...... supplementary angle

» 90 + y + 12 = 180

» y + 102 = 180

» y = 180 - 102

» y = 78

Therefore, the measure of ∠BOD is 78°

Now, Verification

➯ ∠AOC + ∠AOE + ∠COD + ∠BOD + ∠BOE = 360°

➯ 45 + 135 + 90 + 78 + 12 = 360

➯ 180 + 180 = 360

➯ 360 = 360

L.H.S = R.H.S

Hence, Verified !