Adjacent Angles & Vertical Opposite Angles Class 6 Notes | EduRev

Class 6 : Adjacent Angles & Vertical Opposite Angles Class 6 Notes | EduRev

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What are opposite angles and adjacent?
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Adjacent Angles & Vertical Angles

December 3, 20171 Comment

The measure of rotation of a ray, when it is rotated about its end point is known as the angle formed by the ray between its initial and final position.

Adjacent Angles

Consider a wall clock as shown in the following fig. 1. The minute hand and second hand of clock form one angle represented as ∠AOC and the hour hand forms another angle with the second hand represented as∠COB. Both these pair of angles i.e.∠AOC and ∠COB lies next to each other and are known as adjacent angles.

Adjacent Angles & Vertical Opposite Angles Class 6 Notes | EduRev

∠AOC and ∠COB have a common vertex, a common arm and the uncommon arms lie on either side of the common arms. Such angles are known as

adjacent angles.

Here are some examples of Adjacent angles:

Adjacent Angles & Vertical Opposite Angles Class 6 Notes | EduRev

Linear Pair

Pair of adjacent angles whose measures add up to form a straight angle is known as a linear pair. The angles in a linear pair are supplementary.

Consider the following figure in which a ray OPOP→ stand on the line segment AB¯¯¯¯¯¯¯¯AB¯   as shown:

Adjacent Angles & Vertical Opposite Angles Class 6 Notes | EduRev

The angles ∠POB and ∠POA are formed at O. ∠POB and ∠POA are adjacent angles and they are supplementary i.e. ∠POB + ∠POA = ∠AOB = 180°

∠POB and ∠POA are adjacent to each other and when the sum of adjacent angles is 180° then such angles form linear pair of angles.

Vertically Opposite Angles

When a pair of lines intersects, as shown in the fig. below, four angles are formed. ∠AOD and ∠COB are vertically opposite to each other and ∠AOC and ∠BOD are vertically opposite to each other. These angles are also known as vertical angles or opposite angles.

Adjacent Angles & Vertical Opposite Angles Class 6 Notes | EduRev

Thus, when two lines intersect, two pair of vertically opposite angles are formed i.e. ∠AOD, ∠COB and ∠AOC, ∠BOD.

According to vertical angle theorem, in a pair of intersecting lines the vertically opposite angles are equal.

To understand this theorem in detail and to learn more about angles and other concepts please download BYJU’S-The Learning App. Happy Learning!!!

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