5.2.4.38 Various problems on the plane

\( \underline{\mathrm{y}_{\text {word: }}} \) A straight line passing through the midpoints of the diagonals of a quadrilateral forms angles \(50^{\circ}\) and \(80^{\circ}\) with its sides. Prove that the distance between the midpoints of the diagonals is equal to half of one of the sides of the quadrilateral.