PQRS is a square such that PR and SQ intersect at O. State the measure of $∠ P O Q .$

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Solution

In a square PQRS,

Diagonals PR and QS intersects each other at O.

$∵$ The diagonals of a square bisect each other at right angles.

$∴ ∠ P O Q = 90^{\circ}$

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\begin{matrix} Properties & Quadrilaterals In a parallelogram ABCD If ∠ D = 115^{\circ},then the measure of ∠ A = & 68^{\circ} PQRS is a square such that PR and SQ intersect at O then the measure of ∠ P O Q = & 58^{\circ} The diagonals of a rectangle ABCD meet at O. If ∠ B O C = 44^{\circ}, then the measure of ∠ O A D = & 90^{\circ} If ABCD is a rectangle with ∠ B A C = 32^{\circ}, then the measure of ∠ D B C is = & 65^{\circ} \end{matrix}

\begin{matrix} Properties & Quadrilaterals In a parallelogram ABCD If ∠ D = 115^{\circ},then the measure of ∠ A = & 68^{\circ} PQRS is a square such that PR and SQ intersect at O then the measure of ∠ P O Q = & 58^{\circ} The diagonals of a rectangle ABCD meet at O. If ∠ B O C = 44^{\circ}, then the measure of ∠ O A D = & 90^{\circ} If ABCD is a rectangle with ∠ B A C = 32^{\circ}, then the measure of ∠ D B C is = & 65^{\circ} \end{matrix}

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