Linear Pair of Angles in Geometry

What are Linear Pairs of Angles?

In geometry, linear pairs of angles are two angles that are side-by-side and share a common vertex and side. Linear pairs of angles are also referred to as supplementary angles because they add up to 180 degrees. The two angles form a straight line, hence the name linear pair.

For example, two adjacent angles such as ?ABC and ?CBD form a linear pair. The vertex of the pair is point C and the common side is line segment CB.

Types of Linear Pairs of Angles

There are four types of linear pairs of angles. These include complementary angles, supplementary angles, alternate interior angles, and corresponding angles.

Complementary angles are two angles that have a sum of 90 degrees. Supplementary angles are two angles that have a sum of 180 degrees. Alternate interior angles are two angles that are located on opposite sides of a transversal line and form a linear pair. Finally, corresponding angles are two angles that are located on the same side of a transversal line and form a linear pair.

How to Solve Linear Pair of Angles Problems

To solve linear pair of angles problems, you will need to first identify the type of linear pair of angles. Once you have identified the type of linear pair of angles, you can then use the appropriate equation to solve the problem.

For example, if you are presented with a problem involving complementary angles, then you can use the equation A + B = 90 to solve the problem. Similarly, if you are presented with a problem involving supplementary angles, then you can use the equation A + B = 180 to solve the problem.

Examples of Linear Pair of Angles Problems

Let's take a look at some examples of linear pair of angles problems.

1. Find the value of x in the following linear pair of angles: ?ABC and ?CBD.

Solution: Since the two angles form a linear pair, they must add up to 180 degrees. Therefore, we can set up the equation x + (x + 40) = 180. Solving for x gives us x = 70.

2. Find the value of x in the following linear pair of angles: ?PQR and ?QRS.

Solution: Since the two angles form a linear pair, they must add up to 180 degrees. Therefore, we can set up the equation x + (x + 30) = 180. Solving for x gives us x = 75.

3. Find the value of x in the following linear pair of angles: ?MNO and ?ONP.

Solution: Since the two angles form a linear pair, they must add up to 180 degrees. Therefore, we can set up the equation x + (x + 45) = 180. Solving for x gives us x = 67.5.

Practice Problems with Answers

1. Find the value of x in the following linear pair of angles: ?STU and ?TUV.

Solution: x + (x + 50) = 180. Solving for x gives us x = 65.

2. Find the value of x in the following linear pair of angles: ?WXY and ?XYZ.

Solution: x + (x + 30) = 180. Solving for x gives us x = 75.

3. Find the value of x in the following linear pair of angles: ?JKL and ?KLM.

Solution: x + (x + 60) = 180. Solving for x gives us x = 60.

4. Find the value of x in the following linear pair of angles: ?ABC and ?CDE.

Solution: x + (x + 70) = 180. Solving for x gives us x = 55.

5. Find the value of x in the following linear pair of angles: ?QRS and ?RST.

Solution: x + (x + 40) = 180. Solving for x gives us x = 70.

Summary

In this article, we discussed linear pairs of angles in geometry. We discussed what linear pairs of angles are and the four types of linear pairs of angles. We also discussed how to solve linear pair of angles problems and provided five practice problems with answers. Linear pairs of angles are important concepts in geometry, so it is important to understand how to solve linear pair of angles problems.

FAQ

What is a linear pair of angles?

A linear pair of angles is two adjacent angles that form a straight line and add up to 180 degrees.

What is the formula for linear pair of angles?

The formula for linear pair of angles is Angle 1 + Angle 2 = 180 degrees.