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Angle Subtended by an Arc of a Circle on the Circle and at the Center

ℚ

Question

if $∠ B O C = 80 °$ , then the value of $∠ A B O$ is .

80°

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40°

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20°

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60°

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Solution

The correct option is C 20°
Given: $∠ B O C = 80 °$ We know that, an angle subtented by an arc at the centre is double the angle subtented by it at any point on the remaining part of the circle.
$\Rightarrow ∠ B O C = 2 \times ∠ B A C$
$∴ ∠ B A C = 40 °$
$∠ B A O = 20 °$
Consider $Δ A O B,$
$O A = O B = r$
$∠ O A B = ∠ O B A$ ..... (angles opposite equal sides are equal)
Hence, $∠ A B O = 20 °$

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