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Pair Of Angles Worksheets

Pairs of angles are fundamental concepts in geometry that help us understand the relationship between different angles formed when lines intersect or when shapes are created. These pairs include complementary, supplementary, adjacent, and vertically opposite angles, each with distinct properties and significance. 

To begin with, complementary angles are two angles whose measures add up to 90 degrees. They often appear in right-angle triangles or when a right angle is divided into two smaller angles. On the other hand, supplementary angles are two angles whose sum is 180 degrees. These usually occur when two lines form a straight angle or a linear pair.

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Now, we will learn more pairs of angles for grade 6 to grade 8 like linear, vertically opposite and adjacent angles here. Before you know all these pairs of angles there is another important concept which is called ‘angles on a straight line’. The sum of angles on a straight line is 180 degree. Thus, any number of angles on a straight line amounts to 180 degree.

Pair of Angles

Vertically opposite angles:

Vertical angles or vertically opposite angles are opposite angles formed when two lines intersect each other. Thus, two pairs of opposite angles are formed when two lines intersect. Here, the pair of opposite angles are equal. Refer the figure given below for clear understanding.

pair of angles 

Adjacent angles:

Two angles are said to be adjacent, if they have a common vertex and a common arm. The angles should not overlap which means the other arms are lying on the opposite side of the common arm.

Linear pair of angles:

 

RELATED GEOMETRY TOPICS  :  2D Shapes, 3D Shapes, Lines rays line segments and planes, Composing and Decomposing shapes

Pair of Angles Worksheets

Furthermore, adjacent angles share a common side and vertex but do not overlap. They are positioned side-by-side, and understanding them is essential when analyzing geometric shapes and solving problems involving parallel lines and transversals. In contrast, vertically opposite angles are formed when two lines intersect, creating two pairs of opposite angles that are always equal. This property is extremely useful in proving geometric theorems and solving for unknown angles.

Moreover, recognizing these angle relationships allows students and professionals to simplify complex diagrams and solve mathematical problems more efficiently. It also builds a strong foundation for more advanced topics in geometry and trigonometry. For instance, when working with polygons, knowing how angle pairs behave can help in calculating missing angle values and verifying the accuracy of constructions. Therefore, understanding pairs of angles is not only a key skill in academics but also a practical tool in fields such as engineering, architecture, and design.

By mastering these basic relationships, learners can confidently progress to more complex geometric concepts and real-world applications.

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