# Lines and Angles

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 180**

∠AOC + ∠BOC = 180

^{0}.∠AOC + ∠BOC = 180

^{0}.**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

• 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