suppose both pairs of opposite sides of a quadrilateral are parallel. Which angles of the quadrilateral must be supplementary?
To determine which angles of a quadrilateral are supplementary when both pairs of opposite sides are parallel, we need to understand the properties of quadrilaterals with parallel sides.
In a quadrilateral, opposite angles are formed when two lines intersect. If both pairs of opposite sides are parallel, then the two lines that intersect are also parallel.
When two parallel lines are intersected by a third line, known as a transversal, several pairs of angles are formed. These pairs of angles have specific relationships.
In the case of quadrilaterals, when both pairs of opposite sides are parallel, the consecutive interior angles (angles formed on the same side of the transversal and inside the quadrilateral) are supplementary. This means that the sum of the consecutive interior angles is 180 degrees.
Therefore, in a quadrilateral where both pairs of opposite sides are parallel, the consecutive interior angles must be supplementary.