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Lines and AnglesCovid-19 has led the world to go through a phenomenal transition . E-learning is the future today. Stay Home , Stay Safe and keep learning!!! In this chapter of lines and angles, we will learn about pairs of angles which have been given specific names.Lines and Angles 1) Adjacent Angles : Two angles in a plane are adjacent angles, if i) They have a common vertex ii) They have a common arm, and iii) Their other arms lie on the opposite sides of the common arm. ![]() Here, ∠ AOC and ∠BOC have the common vertex O. Also, they have a common arm OC and other arms OB and OA. So, ∠AOC and ∠BOC are adjacent angles. 2) Linear Pair Angles : Two adjacent angles are said to form a linear pair of angles, if their non-common arms are two opposite rays. ![]() Here, OA and OB are two opposite rays and ∠AOC and ∠BOC are the adjacent angles. Therefore, ∠AOC and ∠BOC form a linear pair. The sum of the angles in a linear pair is 1800. ∠AOC + ∠BOC = 1800. 3) Vertically Opposite Angles : Two angles formed by two intersecting lines having no common arm are called vertically opposite angles. Vertically opposite angles have the same measure. They are equal. ![]() Here, AB and CD are intersecting lines and intersection point is O. So 4 angles are formed. Angles ∠1 and ∠3 form a pair of vertically opposite angles; while ∠2 and ∠4 form another pair of vertically opposite angles. Proof of vertically opposite angles are equal. ∠1 and ∠2 form a linear pair. ∠1 + ∠2 = 180 0 ⇒ ∠1 = 180 - ∠2 Also ∠2 and ∠4 form a linear pair. ∠2 + ∠4 = 180 0 ⇒ ∠3 = 180 - ∠2 So from the above, its clear that ∠1 = ∠3 Similarly, ∠2 = ∠4 Angle at a point : Angles formed by a number of rays having a common initial point are called angles at a point. ![]() In the given figure, O is the common point. If you find the measures of these angles 1,2,3 and 4 then it will be ∠1 + ∠2 + ∠3 + ∠4 = 360 0 . Basic Geometry • Point • Lines • Angles • Lines and Angles • Complementary angles • Supplementary angles • Vertically Opposite Angles • Linear Pair Angles • Adjacent Angles • Parallel Lines • Solved Problems on Intersecting Lines • Solved Problems on Parallel Lines 7th grade math Home Page Covid-19 has affected physical interactions between people. Don't let it affect your learning.
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