Squares ABPQ and ADRS are drawn on the sides AB and AD of a parallelogram ABCD. Which of the following options is correct?

$∠ S A Q = ∠ A B C$

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$∠ S R D = ∠ A D C$

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$∠ S A D = ∠ A B C$

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None of these

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Solution

The correct option is A
$∠ S A Q = ∠ A B C$

Let $∠$ DAB = x°

$∠$ ABC = 180° -x …. (adjacent angles of a parallelogram are supplementary) ……….. (i)

$∠$ DAS = $∠$ QAB = 90° (ADRS and ABPQ are squares)

$∠$ SAQ + $∠$ QAB + $∠$ DAB + $∠$ DAS = 360° ……… (angles about a point add to 360°)

$∠$ SAQ + 90°+ x° + 90° = 360°

$∠$ SAQ = 180° - x

Hence $∠$ SAQ = $∠$ ABC ….. from(i)

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