What is the relationship between the measures of angles in a linear pair?

The relationship between the measures of angles in a linear pair is that they are supplementary. In other words, the sum of the measures of the two angles in a linear pair is always equal to 180 degrees. This relationship holds true for any pair of adjacent angles that form a straight line.

To understand and visualize this relationship, you can follow these steps:

1. Draw a straight line (also known as a straight angle) on a piece of paper or imagine it in your mind.
2. Choose any point on the line and draw two rays (half-lines) extending from that point in opposite directions.
3. The two rays will form an angle at the vertex (the common endpoint of the rays).
4. This angle, along with its adjacent and supplementary angle, form a linear pair.
5. Measure the two angles using a protractor or by estimating their sizes visually.
6. Add the measures of the two angles together.
7. The sum of the two angle measures should equal 180 degrees.

By following these steps, you can observe the relationship between the measures of angles in a linear pair and confirm that they are always supplementary.

In geometry, a linear pair consists of two adjacent angles whose measures add up to 180 degrees. The relationship between the measures of angles in a linear pair can be summarized as follows:

1. Supplementary angles: The two angles in a linear pair are always supplementary, meaning that their measures add up to 180 degrees. For example, if one angle measures 85 degrees, the other angle in the linear pair would measure 180 - 85 = 95 degrees.

2. Equal measures: The angles in a linear pair do not have to have equal measures. They can be different sizes, as long as their measures add up to 180 degrees. However, if one angle is a right angle (90 degrees), the other angle in the linear pair must also be a right angle, making them equal in measure.

3. Adjacent angles: A linear pair consists of two adjacent angles, which means they share a common vertex and a common side. The non-common sides of the two angles form a straight line, creating a 180-degree angle at their shared vertex.

So, in summary, the measures of angles in a linear pair are always supplementary, can be equal or different, and are always adjacent angles.