Understanding Adjacent Supplementary Angles and How to Find Their Measures

Adjacent Supplementary Angles

Adjacent supplementary angles are a pair of angles that share a common vertex and side, and their measures add up to 180 degrees

Adjacent supplementary angles are a pair of angles that share a common vertex and side, and their measures add up to 180 degrees. Adjacent angles are angles that are side by side, whereas supplementary angles are angles that add up to 180 degrees.

To better understand adjacent supplementary angles, let’s consider an example. Take a straight line, and mark a point on it, which we will call the vertex. From this vertex, draw two rays that form an angle. The angle that is formed by these two rays can be split into two adjacent supplementary angles.

For example, let’s say we have a vertex P. From this point, we draw two rays: PA and PB. The angle formed by these rays is angle APB. In this case, angles APB and BPA are adjacent supplementary angles because they share a common vertex (P) and a common side (PB), and their measures add up to 180 degrees.

It is important to note that adjacent supplementary angles do not have to be equal in measure. They can have different measures, as long as the sum of their measures adds up to 180 degrees.

To find the measures of adjacent supplementary angles, we can use the fact that their measures add up to 180 degrees. So, if we know the measure of one of the angles, we can find the measure of the other by subtracting the known measure from 180 degrees.

For example, if angle APB has a measure of 120 degrees, we can find the measure of angle BPA by subtracting 120 from 180: 180 – 120 = 60 degrees. Therefore, angle BPA measures 60 degrees.

In summary, adjacent supplementary angles are a pair of angles that share a common vertex and side, and their measures add up to 180 degrees. They can have different measures, and to find the measure of one angle, we can subtract the measure of the other from 180 degrees.

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