# 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° Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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