TRANSVERSAL LINES

A straight line that intersects two or more straight lines at distinct points is called as transversal.

More clearly, 

A straight line intersecting two 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°

Same side exterior angles are supplementary.

 1 +  8  =  180°

 2 +  7  =  180°

Practice Problems

Problem 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°

Substitute F  =  65°.

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°

Problem 2 :

In the figure given below,  let the lines l1 and lbe 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, 

2x + 20  =  3x - 10

30  =  x

Problem 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, 

3x + 20 + 2x  =  180°

5x + 20  =  180°

5x  =  160°

x  =  32°

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