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In the given figure, O is the centre of a circle in which OAB

Question

In the given figure, $O$ is the centre of a circle in which $∠ O A B = 2 0^{o}$ and $∠ OCB = 5 5^{o}$ . Find
$∠ A OC$

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Elijah Discussed

In the given figure,

O

is the centre of a circle in which

∠ O A B = 2 0^{o}

and

∠ OCB = 5 5^{o}

. Find

∠ A OC

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

We know that

O A = OB

which is the radius

The base angles of an isosceles triangle are equal

So we get

∠ OB A = ∠ O A B = 2 0^{o}

△ A OB

Using the angle sum property

∠ A OB + ∠ O A B + ∠ OB A = 18 0^{o}

By substituting values

∠ A OB + 2 0^{o} + 2 0^{o} = 18 0^{o}

On further calculation

∠ A OB = 18 0^{o} - 2 0^{o} - 2 0^{o}

By subtraction

∠ A OB = 18 0^{o} - 4 0^{o}

So we get

∠ A OB = 14 0^{o}

We know that

∠ A OC = ∠ A OB - ∠ BOC

By substituting the values

∠ A OC = 14 0^{o} - 7 0^{o}

So we get

∠ A OC = 7 0^{o}

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Question Text	In the given figure, $O$ is the centre of a circle in which $∠ O A B = 2 0^{o}$ and $∠ OCB = 5 5^{o}$ . Find $∠ A OC$
Answer Type	Text solution:1
Upvotes	150

In the given figure, O is the centre of a circle in which ∠OAB=20o and ∠OCB=55o. Find ∠AOC

Text solutionVerified

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In the given figure, $O$ is the centre of a circle in which $∠ O A B = 2 0^{o}$ and $∠ OCB = 5 5^{o}$ . Find
$∠ A OC$