Alternate Exterior Angles

Definition of Alternate Exterior Angles

When two lines are cut by another line (transversal), the pairs of angles formed outside the two lines and on the opposite of the transversal are called Alternate Exterior Angles.

More about Alternate Exterior Angles

If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.

Examples of Alternate Exterior Angles

example of Alternate Exterior Angles

AB || CD and EF is the transversal cutting the parallel lines. So, ∠2 and ∠8, ∠1 and ∠7 are the pairs of alternate exterior angles in the figure shown.


Video Examples: Alternate Exterior Angles


Solved Example on Alternate Exterior Angles

Ques:

PQ and RS are two lines and UT is a transversal of PQ and RS. Which among the following is a pair of alternate exterior angles?
Example of Alternate Exterior Angles

Choices:
  • A. ∠4 and ∠5
  • B. ∠2 and ∠8
  • C. ∠1 and ∠2
  • D. ∠1 and ∠8

Correct Answer: D

Solution:

  • Step 1: When two lines are cut by another line (transversal), the pairs of angles formed outside the two lines and on the opposite of the transversal are called Alternate Exterior Angles.
  • Step 2: From the figure, PQ and RS are parallel lines and UT is a transversal passing through the parallel lines.
  • Step 3: The pairs of alternate exterior angles are
  • ∠1 and ∠8
    ∠2 and ∠7
  • Step 4: Hence, ∠1 and ∠8 are the alternate exterior angles in the given figure.

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