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 .
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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 .
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 ° .
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Substitute and solve.
140 ° + m ∠ C Y E = 180 ° 140 ° + m ∠ C Y E − 140 ° = 180 ° − 140 ° m ∠ C Y E = 40 °