The opposite sides of the quadrilateral ABCD are parallel in pairs.

The opposite sides of the quadrilateral ABCD are parallel in pairs. Find the angles and lengths of the sides of this quadrilateral, if A = 30 °, AB = 2cm, BC = 4cm

If the opposite sides of a quadrilateral are pairwise parallel, then such a quadrilateral is a parallelogram. Therefore, its opposite sides are not only parallel, but also equal: AB = CD = 2 cm, BC = AD = 4 cm. The opposite angles of the parallelogram are also equal, that is, ∠A = ∠C = 30 °, ∠B = ∠C. The sum of the angles of the quadrilateral is 360 °, then ∠B + ∠C = 360 ° – ∠A – ∠C = 360 ° – 30 ° – 30 ° = 300 °. Then ∠B = ∠C = 300 ° / 2 = 150 °.