In geometry, a transversal is a line the intersects 2 or much more other (often parallel ) lines.

In the number below, line n is a transversal cut lines l and m .

as soon as two or much more lines are cut by a transversal, the angles which occupy the exact same relative position are dubbed corresponding angles .

In the figure the bag of corresponding angles are:

∠ 1 and ∠ 5 ∠ 2 and ∠ 6 ∠ 3 and ∠ 7 ∠ 4 and ∠ 8

when the lines are parallel, the corresponding angles space congruent .

when two lines are reduced by a transversal, the pairs of angles on one side of the transversal and also inside the two lines are dubbed the consecutive interior angles .

In the over figure, the consecutive internal angles are:

∠ 3 and ∠ 6 ∠ 4 and also ∠ 5

If two parallel currently are cut by a transversal, then the bag of consecutive interior angles developed are supplementary .

when two currently are reduced by a transversal, the bag of angles on either side of the transversal and also inside the two lines are referred to as the alternate interior angle .

In the over figure, the alternative interior angles are:

∠ 3 and ∠ 5 ∠ 4 and also ∠ 6

If 2 parallel currently are cut by a transversal, climate the alternate interior angles developed are congruent .

as soon as two currently are cut by a transversal, the pairs of angles on either next of the transversal and outside the two lines are referred to as the alternative exterior angles .

In the above figure, the alternative exterior angle are:

∠ 2 and also ∠ 8 ∠ 1 and also ∠ 7

If 2 parallel lines are reduced by a transversal, then the alternating exterior angles developed are congruent .

You are watching: A line that intersects two or more lines

instance 1:

In the above diagram, the present j and k are reduced by the transversal together . The angle ∠ c and ∠ e are…

A. Corresponding Angles

B. Consecutive internal Angles

C. Alternative Interior angles

D. Alternate Exterior angle

The angle ∠ c and ∠ e lied on either side of the transversal l and also inside the two lines j and also k .

Therefore, castle are alternating interior angles.

The correct an option is C .

instance 2:

In the above figure if currently A B ↔ and C D ↔ room parallel and also m ∠ A X F = 140 ° then what is the measure of ∠ C Y E ?

The angles ∠ A X F and also ∠ C Y E lie on one next of the transversal E F ↔ and also inside the 2 lines A B ↔ and C D ↔ . So, they space consecutive interior angles.

due to the fact that the currently A B ↔ and also C D ↔ space parallel, by the consecutive interior angles theorem , ∠ A X F and ∠ C Y E are supplementary.

the is, m ∠ A X F + m ∠ C Y E = 180 ° .

But, m ∠ A X F = 140 ° .

See more: The Hotel Franklin Roosevelt Hotel Paris, Hotel Franklin Roosevelt Paris

Substitute and solve.

140 ° + m ∠ C Y E = 180 ° 140 ° + m ∠ C Y E − 140 ° = 180 ° − 140 ° m ∠ C Y E = 40 °