# Linear Pair of Angles

What is linear pair of angles?

Two angles form a linear pair if they have;

A common arm

A common vertex

Their interiors do not overlap

The sum of two angles is 180°.

Therefore, linear pair of angles are adjacent angles whose non-common arms are opposite rays.

Note:

All adjacent angles do not form a linear pair.

From the above figure we can observe; OX and OY are two opposite rays and ∠XOZ and ∠YOZ are the adjacent angles. Therefore, ∠XOZ and ∠YOZ form a linear pair.

If you measure ∠XOZ and ∠YOZ with the help of the protractor, you will find the sum of their measures equal to 180°.

Thus, the sum of the angles in a linear pair is 180°.

Worked-out problems on Linear Pair of angles:

In the given figure, ∠AOC and ∠ BOC form a linear pair if x - y = 60°, find the value of x and y.

Solution:

Given x - y = 60° ………… (i)

We know that, x + y = 180° ………… (ii)

2x = 240°

x = 240°/2

Therefore, x = 120°

Since, x - y = 60°

or, 120° - y = 60°

or, 120° - 120° - y = 60° - 120°

or, -y = -60°

Therefore, y = 60°

Lines and Angles

Fundamental Geometrical Concepts

Angles

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Relation between Diameter Radius and Circumference |Problems |Examples

Apr 22, 24 05:19 PM

Relation between diameter radius and circumference are discussed here. Relation between Diameter and Radius: What is the relation between diameter and radius? Solution: Diameter of a circle is twice

2. ### Circle Math | Terms Related to the Circle | Symbol of Circle O | Math

Apr 22, 24 01:35 PM

In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

3. ### Preschool Math Activities | Colorful Preschool Worksheets | Lesson

Apr 21, 24 10:57 AM

Preschool math activities are designed to help the preschoolers to recognize the numbers and the beginning of counting. We believe that young children learn through play and from engaging

4. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Apr 20, 24 05:39 PM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

5. ### What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

Apr 20, 24 05:29 PM

In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other