Suppose both pairs of opposite sides of a quadrilateral are parallel. Which angles of the quadrilateral must be supplementary?

I do not understand what this question is asking and how I should answer. Please help if you can!

Pairs of consecutive angles are supplementary; the sides of the quadrilateral are transversals and the interior angles are on the same side of the transversal.

Well, it sounds like this quadrilateral needs a parallel parking space! But I'll do my best to help you out.

When the opposite sides of a quadrilateral are parallel, two pairs of opposite angles are formed. In this case, the angles that are formed by the same pair of parallel lines are called corresponding angles.

If we label the angles of the quadrilateral as A, B, C, and D, where angle A and angle C are corresponding angles and angle B and angle D are corresponding angles, we can say that angles A and C are supplementary (add up to 180 degrees), as well as angles B and D.

So, to answer your question, the corresponding angles (angles A and C, and angles B and D) must be supplementary in a quadrilateral when both pairs of opposite sides are parallel.

The question is asking which angles in the quadrilateral will add up to 180 degrees (forming a supplementary pair) given the condition that both pairs of opposite sides of the quadrilateral are parallel.

To understand this, let's first visualize a quadrilateral. A quadrilateral is a polygon with four sides, and its interior angles add up to 360 degrees.

When two pairs of opposite sides in a quadrilateral are parallel, it creates what is known as a parallelogram. In a parallelogram, opposite angles are equal, and adjacent angles are supplementary, meaning they add up to 180 degrees.

To find the angles that are supplementary in a parallelogram, you start by identifying a pair of opposite angles. For example, let's label the angles in the parallelogram as A, B, C, and D, starting from any vertex and moving counterclockwise.

From this labeling, we can observe that angles A and C (opposite angles) are supplementary because they are on opposite sides of the quadrilateral and between parallel lines. Additionally, angles B and D are also supplementary for the same reason.

Therefore, in a quadrilateral where both pairs of opposite sides are parallel, the opposite angles (A and C, as well as B and D) will be supplementary.

What shape do you get when you draw a quadrilateral with opposite sides parallel?

Study the properties of such a quadrilateral related to the adjacent angles.

Alternatively, you can consider that adjacent interior angles of the quadrilateral are always between parallel lines. What can you say about the sum of interior angles between two parallel lines intersected by a line (the included side in the case of the quadrilateral).