Question

In a quadrilateral PQRS, the diagonals PR and QS bisect each other. If ∠Q = 56°, determine ∠R.

Answer 1

Since, the diagonals PR and QS of quadrilateral PQRS bisect each other. (Given)

So, PQRS is a parallelogram.

Now, $\angle Q+\angle R=180°$(Adjacent angles are supplementary.)

$$\begin{gathered} \Rightarrow 56°+\angle R=180° \\ \Rightarrow \angle R=180°-56° \\ \Rightarrow \angle R=124° \end{gathered}$$