# PARALLEL LINES AND TRANSVERSALS

## About "Parallel lines and transversals"

Parallel lines and transversals

A transversal is a line that intersects two lines in the same plane at two different points. Transversal and lines l₁ and l₂ form eight angles.

More clearly,

Here, l₁ and l₂ are parallel lines.

From the above figure, we have the following important points.

 Vertically opposite angles are equal. < 1  =  < 3  < 2  =  < 4  < 5  =  < 7  < 6  =  < 8
 Corresponding angles are equal. < 1  =  < 5  < 2  =  < 6  < 3  =  < 7  < 4  =  < 8
 Alternate interior  angles  are equal. < 3  =  < 5  < 4  =  < 6
 Alternate exterior angles  are equal. < 1  =  < 7  < 2  =  < 8
 Consecutive interior angles are supplementary. < 3 + < 6  =  180°< 4 + < 5  =  180°

## Parallel lines and transversals - Examples

Example 1 :

In the figure given below,  let the lines l₁ and l₂ be parallel and m is transversal. If F  =  65°, find the measure of each of the remaining angles.

Solution :

From the given figure,

F and H are vertically opposite angles and they are equal.

Then, H  =  F -------> H  =  65°

H and D are corresponding angles and they are equal.

Then, D  =  H -------> D  =  65°

D and B are vertically opposite angles and they are equal.

Then, B  =  D -------> B  =  65°

F and E are together form a straight angle.

Then, we have

F + E  =  180°

Plug F  =  65°

F + E  =  180°

65° + E  =  180°

E  =  115°

E and G are vertically opposite angles and they are equal.

Then, G  =  E -------> G  =  115°

G and C are corresponding angles and they are equal.

Then, C  =  G -------> C  =  115°

C and A are vertically opposite angles and they are equal.

Then, A  =  C -------> A  =  115°

Therefore,

A  =  C  =  E  =  G  =  115°

B  =  D  =  F  =  H  =  65°

Example 2 :

In the figure given below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x"

Solution :

From the given figure,

(2x + 20)° and (3x - 10)° are corresponding angles.

So, they are equal.

Then, we have

2x + 20  =  3x - 10

30  =  x

Hence, x  =  30°

Example 3 :

In the figure given below,  let the lines l₁ and l₂ be parallel and t is transversal. Find the value of "x".

Solution :

From the given figure,

(3x + 20)° and 2x° are consecutive interior angles.

So, they are supplementary.

Then, we have

3x + 20 + 2x  =  180°

5x + 20  =  180°

5x  =  160°

x  =  32°

Hence, x  =  32°

After having gone through the stuff given above, we hope that the students would have understood "Parallel lines and transversals".

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