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Angles in Alternate Segments

If O is cen...

Question

If $O$ is centre of circle as shown in figure, find $∠ R T O$ if $∠ Q R T = 30^{\circ}$

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Solution

The angles on the same line sum up to give $180$

$⟹ ∠ P O T + ∠ T O Q = 180 ∠ T O Q = 180 - 140 = 40^{\circ}$

Consider $Δ R T O$

Sum of angles is $180$

$⟹ 40 + 30 + ∠ R T O = 180 ∠ R T O = 110^{\circ}$

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