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Condition for Two Lines to Be Parallel

In figure ,if...

Question

In figure ,if $Q T ⊥ P R, ∠ T Q R = 40^{o}$ and $∠ S P R = 30^{o}$ ,then y is

70^{o}

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110^{o}

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90^{o}

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80^{o}

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Solution

The correct option is D $80^{o}$
$∠ M T P + ∠ T P M = ∠ T M S$
$30 + 90 = ∠ T M S$
$∠ T M S = 120^{o}$
$∠ Q + ∠ M + ∠ S = 180^{o}$
$y = 180^{o} - (100) = 80^{o}$

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∠ S P R = 30^{o}

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x

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In figure, if QT is perpendicular to PR, $∠ T Q R = 40^{\circ}$ and $∠ S P R = 30^{\circ}$ , find x and y.

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