Understanding Supplementary Angles in a Linear Pair: A Simple Guide

Two angles that form a linear pair are supplementary, meaning their measures add up to 180 degrees. In this guide, we will explore how to determine the measure of the other angle when one angle measures 122 degrees.

What Are Supplementary Angles?

Supplementary angles are two angles whose measures add up to 180 degrees. In a linear pair, these angles are adjacent and lie on a straight line. Adjacent angles are angles that share a common vertex and side but do not overlap.

Calculating the Measure of the Other Angle

If one angle in a linear pair measures 122 degrees, we can find the measure of the other angle by subtracting 122 degrees from 180 degrees. Here's the step-by-step process:

Start with the total measure of supplementary angles: 180 degrees. Subtract the known angle: 180 - 122 58 degrees.

Therefore, the measure of the other angle is 58 degrees.

Mathematically, if one angle is 122 degrees, the other angle can be calculated as follows:

Measure of the other angle 180 - 122 58 degrees

Problem Solving Practice

Let's go through a few examples to understand the application of this concept:

Example 1: Let the other angle be x. Since the sum of the angles forming a linear pair is 180 degrees, we have the equation: 180 122 x. Subtract 122 from both sides: x 180 - 122 58 degrees.

Therefore, the angle that forms a linear pair with an angle measuring 122 degrees is 58 degrees.

Example 2: Given that the sum of supplementary angles is 180 degrees: 180 - 122 58 degrees.

The other angle in the linear pair is 58 degrees.

Conclusion

Understanding how to calculate the measure of the other angle in a linear pair is essential for many applications. This concept is fundamental in geometry and helps in solving complex problems related to angles and lines. By following the steps outlined in this guide, you can easily determine the angle measurements in a linear pair.

Key Takeaways

Supplementary angles add up to 180 degrees. In a linear pair, the angles are adjacent and form a straight line. Calculate the measure of the other angle using the equation: 180 - known angle.

For further practice and more detailed explanations, refer to additional resources on geometry and angle measurement.