Question

(c) In the given figure, lengths of arcs APB and BQC are in the
ratio 5:3 and angle AOC = 152°: find angle ACB and angle
BAC

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Answer 1

Answer:

The measure of angle ∠ACB is 282° and

The measure of angle ∠BAC is 230° .

Step-by-step explanation:

Given as :

The circle with center O

The measure of angle ∠AOC = 152°

The ratio of length of arc APB : The length of arc BQC = 5 : 3

So, The length of arc APB = 5 x

And The length of arc BQC = 3 x

Let The measure of angle ∠ACB = a°

Let The measure of angle ∠BAC = b°

According to question

∵ The measure of angle ∠AOC = 152°

So, The reflex angle ∠AOC = 360° - 152° = 208°

And ∠AOB : ∠BOC = 5 : 3

i.e 2 ∠AOB = 2 ∠BOC

So , 3 x + 5 x = 208°

Or, 8 x = 208°

∴ x = $\dfrac{208}{8}$

i.e  x = 26°

So, ∠AOB = 3 × 26° = 78°

And ∠BOC = 5 × 26° = 130°

∴ ∠ACB = ∠AOC + ∠BOC

Or, ∠ACB = 152° + 130°

∴ ∠ACB = 282°

And

∠BAC = ∠AOB + ∠AOC

I.e ∠BAC = 78° + 152° = 230°

Hence, The measure of angle ∠ACB is 282° and The measure of angle ∠BAC is 230° . Answer