Question

Find <BOC in the given figure​

Answer 1

$\color{purple}{\boxed {\</strong><strong>huge</strong><strong>{ \mathtt{∠BOC = 100 \degree }}}}$

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Given :-

• ∠CAO = 20°
• ∠CBO = 30°

To find :-

• ∠BOC = ?

Construction:-

• Join OC

So after that :-

• AO = OC ( ∵ Radius of circle )

∴ ∠ACO = 20°

∴ ∠BCO = 30°

So,

$\mathtt{\implies{∠ACB = ∠ACO + ∠BCO}}$

$\mathtt{ \implies{∠ACB =20 \degree+ 30 \degree}}$

$\large \color{green}\mathtt{\implies∠ACB = 50 \degree}$

∠BOC = It is double of angle ACB beacuse of theorem.

• {The angle substanded by an arc at the centre of the circle is twice the angle substanded by the same arc at any other point on the circle.}

$\large \mathtt{∴∠BOC = 2(∠ACB ) }$

$\large \mathtt{∴∠BOC = 2(50 \degree ) }$

$\color{purple}{\boxed {\large{ \mathtt{∴∠BOC = 100 \degree }}}}$

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