# In the given figure the length of acrs AB and BC are in the ratio 3:2 if angle AOB = 96^ find : angle BOC and ABC

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## Answers

Answered by

47

## Solution :-

Let Arc AB = 3x

Let Arc BC = 2x

∠by 3x = 96°

∠by x = 96/3 = 32°

∠by 2x = 32 × 2 = 64°

So,

### ∠BOC = 64°

OA = OB = BC

⟹ ∠OAB = ∠CBA = x

∠OBC = ∠OCB = y

(∠in front of equal sides)

In △ ACB

⟹ x + x + 96 = 180°

⟹ 2x = 84

⟹ x = 84/2

⟹ x = 42°

In △ BOC

y + y + 64 = 180°

⟹ 2y = 116

⟹ y = 116/2

⟹ y = 58°

So,

### ∠ABC = x + y

### = 42 + 58

### = 100°

__Therefore____,__

## ∠BOC = 64°

## ∠ABC = 100°

Attachments:

Answered by

60

Solution :-

Let Arc AB = 3x

Let Arc BC = 2x

∠by 3x = 96°

∠by x = 96/3 = 32°

∠by 2x = 32 × 2 = 64°

So,

∠BOC = 64°

OA = OB = BC

⟹ ∠OAB = ∠CBA = x

∠OBC = ∠OCB = y

(∠in front of equal sides)

In △ ACB

⟹ x + x + 96 = 180°

⟹ 2x = 84

⟹ x = 84/2

⟹ x = 42°

In △ BOC

y + y + 64 = 180°

⟹ 2y = 116

⟹ y = 116/2

⟹ y = 58°

So,

∠ABC = x + y

= 42 + 58

= 100°

Therefore,

∠BOC = 64°

∠ABC = 100°

*HOPE** **SO** **IT** **WILL** **HELP**.**.**.**.**.*

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