In the given figure, what is the angle subtended by chord AB at the point C on the circle?

60^{\circ}

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65^{\circ}

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55^{\circ}

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70^{\circ}

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Solution

The correct option is C $55^{\circ}$
Note that $∠ A C B$ is the angle subtended by the chord AB at the point C on the circle.
Using angle sum property in $△ A B C,$ we have
$∠ A B C + ∠ A C B + ∠ B A C = 180^{\circ} .$
$⟹ 60^{\circ} + ∠ A C B + 65^{\circ} = 180^{\circ}$
$⟹ ∠ A C B = 180^{\circ} - 125^{\circ} = 55^{\circ}$

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In the given figure, what is the angle subtended by chord AB at the point C on the circle?

The correct option is C 55∘Note that ∠ACB is the angle subtended by the chord AB at the point C on the circle. Using angle sum property in △ABC, we have ∠ABC+∠ACB+∠BAC=180∘. ⟹60∘+∠ACB+65∘=180∘ ⟹∠ACB=180∘−125∘=55∘