Question

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

Answer 1

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°

Answer 2

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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.....