Question:
In a quadrilateral PQRS, the diagonals PR and QS bisect each other. If ∠Q = 56°, determine ∠R.
Solution:
Since, the diagonals PR and QS of quadrilateral PQRS bisect each other. (Given)
So, PQRS is a parallelogram.
Now, $\angle Q+\angle R=180^{\circ}$ (Adjacent angles are supplementary.)
$\Rightarrow 56^{\circ}+\angle R=180^{\circ}$
$\Rightarrow \angle R=180^{\circ}-56^{\circ}$
$\Rightarrow \angle R=124^{\circ}$
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