In this section we discuss about angles are **formed by Parallel Lines Cut by a Transversal line** like *corresponding angles, Alternate interior lines, Alternate exterior angles , co interior angles and co exterior angles*. Also learn about properties of the same angles.

### Interior angles | Exterior Angles | Alternate Interior and Alternate Exterior Angles

Contents

**What is Transversal Line**

The *transversal line* is defined as ” A line which intersects two or more lines at distinct points”.

**For example**

**Fig -1 :** Here lines** ‘ n’ & ‘ m’ ** are parallel lines and a line ‘* l’ *intersection both lines at distinct points so a line ‘ l’ is a

*transversal*to given lines of ‘n’ and ‘ m’

**Fig -2 :** Here lines ‘** n’ & ‘ m’ ** are non-parallel lines and a line ‘** l’** intersection both lines at distinct points so a line

**‘ l**‘ is a

*transversal*to given lines of

**‘n’**and ‘

**m’**

**Fig – 4 :** Here line **‘l ‘** is not a *transversal*

Here **‘ l’** is a transversal for the lines of ‘** m’** and ‘** n**‘.

Total eight Angles are formed by **parallel lines and transversal Line**. Also same eight angles are formed by non-parallel lines and transversal line

So from the above figures angles are formed as follows

**∠1 , ∠2 , ∠3 , ∠4 , ∠5 , ∠6 , ∠7 & ∠8**

### Interior Angles

In the above figure **∠3 , ∠4 , ∠5 & ∠6** are called **interior angles** since those angles lie in between two lines.

i.e interior of two lines

### Exterior Angles

In the above figure **∠1 , ∠2 , ∠7 & ∠8** are called **exterior angles** since those angles do not lie in between two lines.

i.e outsider of the two lines.

#### Corresponding angles:

In the above figure (** ∠1 , ∠5 ) , ( ∠2 , ∠6 ) , ( ∠3 , ∠7) , (∠4 ∠8)** are the corresponding angles.

i.e Two angles are said to be a pair of* corresponding angles* if

1. They are on the same side of the transversal

2. One is an interior angles and the other is an exterior angle.

3. They are not adjacent angles.

#### Alternate interior angles and Alternate exterior angles

Two angles are said to be* alternate interior angles* if

1. Both are interior angles

2. They are on either side of the transversal

3. They are not adjacent angles

So in the below figure** ( ∠4 , ∠6) , ( ∠3 , ∠5 )** are *alternate interior angles*

Two angles are said to be *alternate exterior angles* if

1. Both are exterior angles

2. They are on either side of the transversal

3. They are not adjacent angles

So in the above figure **( ∠1 , ∠7) , ( ∠2, ∠8)** are *alternate exterior angles*

#### Co-interior angles and Co-exterior angles

Two angles are said to be *Co-interior angles* if they are* interior angles* and lies on same side of the transversal. The Co-interior angles also called as** consecutive angles or allied interior angles.**

So in the below figure **( ∠4, ∠5) , ( ∠3, ∠6)** are *Co-interior angles* or *consecutive angles* or *allied interior angles.*

Two angles are said to be **Co-exterior angles** if they are exterior angles and lies on same side of the transversal.

So in the above figure **( ∠1 ∠8 ) , ( ∠2, ∠7 )** are **Co-exterior angles.**

##### Linear Pair of Angles

If the sum of two adjacent angles is 180^{o}, then they are called a **linear pair of angles.**

In the below figure (** ∠1 , ∠4 ) , ( ∠1 , ∠2 ) , ( ∠2 , ∠3 ) , ( ∠3 , ∠4 ) , ( ∠5 , ∠6) , ( ∠5 , ∠8), (∠6 ∠7) , & (∠7 ∠8)** are linear pair of angles. Hence their sum is **180 ^{o}**. i.e

∠1 + ∠4 = 180^{o }, ∠1 + ∠2 = 180^{o }, ∠2 + ∠3 = 180^{o }, ∠3 + ∠4 = 180^{o}

& ∠5 + ∠6 = 180^{o }, ∠5 + ∠8 = 180^{o }, ∠6 + ∠7 = 180^{o }, ∠7 + ∠8 = 180^{o}

##### Vertical Opposite angles

In the above figure **( ∠1 , ∠3 ) , ( ∠2 , ∠4 ) , ( ∠5 , ∠7 ) , ( ∠6 , ∠8 ) ** are *Vertical Opposite angles.*

We know that if two lines intersect each other, then the vertically opposite angles are equal. Hence these pairs of angles are equal

∠1 = ∠3 , ∠2 = ∠4 , ∠5 = ∠7 & ∠6 = ∠8

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Types of Quadrilateral with their properties and formulas

Properties of circle in math | Arc, Perimeter, Segment of circle

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