Transversal line is a straight line that cuts 2 or more lines. The lines may or may not be parallel. If the lines are parallel, then transversals tell us a great deal about the angles.

The transversal line makes angles equals to 90^{0}, if the lines are perpendicular.

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A line that crosses two or more lines in the same plane is known as transversal to those lines. Whenever a pair of lines are cut by a transversal, 8 angles are formed at the two points of intersection.

A transversal is a line that passes through two lines in the same plane at different points. There are certain pairs of angles are created by lines and transversal with different vertices are given special names.

**Interior Angles:** The angles which lie in between given lines.

In figure: $\angle$3, $\angle$ 4, $\angle$ 5 and $\angle$6 are interior angles since they lie in between lines a and b.

**Exterior Angles:** The angles which do not lie in between given lines.

In figure:** **$\angle$ 1, $\angle$ 2, $\angle$ 7 and $\angle$ 8 are the exterior angles since they do not lie in between lines a and b.

**Alternate Interior Angles:** Two angles formed by transversal with two lines are said to be alternate interior angles if

In figure: $\angle$4 , $\angle$ 5 and $\angle$ 3, $\angle$ 6 are pairs of interior angles.

**Alternate Exterior Angles: **Two angles formed by a transversal with two lines are said to be alternate exterior angles if

In figure: $\angle$1 , $\angle$ 8 and $\angle$ 2, $\angle$ 7 are pairs of exterior angles.

**Corresponding Angles:**

In figure: The pairs of corresponding angles are $\angle$ 1, $\angle$ 6; $\angle$ 4, $\angle$ 7; $\angle$ 2, $\angle$ 5; and $\angle$ 3, $\angle$ 8.

**Co-interior Angles:**

In figure: The pair of co-interior angles are $\angle$ 4, $\angle$6 and $\angle$ 3, $\angle$ 5.

**Co-exterior Angles:**

In figure: The pair of co-exterior angles are $\angle$ 1, $\angle$7 and $\angle$ 2, $\angle$ 8.

### Solved Examples

**Question 1: **

** Solution: **
^{0} is same as 45^{0} (Vertical opposite angles)

**Question 2: **

** Solution: **

A transversal is a line that passes through two lines in the same plane at different points. There are certain pairs of angles are created by lines and transversal with different vertices are given special names.

- both the angles are interior angles
- angles lie on the opposite sides of the transversal
- angles do not form a linear pair.

In figure: $\angle$4 , $\angle$ 5 and $\angle$ 3, $\angle$ 6 are pairs of interior angles.

- both the angles are exterior angles
- angles lie on opposite sides of the transversal
- angles do not form a linear pair.

In figure: $\angle$1 , $\angle$ 8 and $\angle$ 2, $\angle$ 7 are pairs of exterior angles.

In figure: The pairs of corresponding angles are $\angle$ 1, $\angle$ 6; $\angle$ 4, $\angle$ 7; $\angle$ 2, $\angle$ 5; and $\angle$ 3, $\angle$ 8.

In figure: The pair of co-interior angles are $\angle$ 4, $\angle$6 and $\angle$ 3, $\angle$ 5.

In figure: The pair of co-exterior angles are $\angle$ 1, $\angle$7 and $\angle$ 2, $\angle$ 8.

Given below explains the transversal and pairs of lines.**Parallel Lines Cut by a Transversal Line**

In the above figure, AB and XY are parallel to each other and PQ is a transversal line.

There is a relation between the angles in M and N.

**Non Parallel Lines Cut by a Transversal Line**

In the above figure, AB and XY are not parallel to each other and PQ is a transversal line.

There is no relation between angles in M and N.

**Parallel Lines Cut by a Perpendicular Transversal Line**

The perpendicular transversal is a transversal which is perpendicular to the parallel lines and makes all angles equal to 90^{0 }.

In the above figure, AB and XY are parallel to each other and PQ is a transversal line. All angles in M and N are equal to 90^{0 .}

Identify the missing angles in the following figure.

Given one of the angle of M is 45^{0}

From the figure, we can say AB is a straight line,

So, x^{ 0 }+ 45^{0 }= 180^{0}

Subtract 45^{0 }on both sides,

x^{ 0 }+ 45^{0 }- 45^{0 }^{}= 180^{0 }- 45^{0}

x^{ 0 }= 135^{0 .}

The left out angle is same as angle x^{0 }.

The angles of M are related to angles of N.

So, the resultant figure is

Identify the specified angle from the following figure:

In the given figure there are no parallel lines.

Given the angle b is 60^{o}.

We know that the angle of a straight line is 180^{0}.

So, a^{0} + b^{0 }= 180^{0}

a^{0} + 60^{0} = 180^{0}

Subtract 60^{0} on both sides

a^{0 }= 120^{0}.

=> $\angle$ AMN = 60^{o} and $\angle$ BMN = 120^{o}. (Vertical opposite angles)

Since there is no relation between these two lines, thus we cant find the rest of the angles.

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