Two lines are cut by a transversal such that a pair of alternate interior angles are right angles are the two lines parallel

yes. consider the consecutive interior angles.

What is the measure of angle x?

A pair of parallel lines is cut by a transversal. An exterior angle on the left of the transversal is labeled as 40 degrees. An interior angle on the right of the transversal, which is not vertically opposite to the 40 degree angle, is labeled as x.

What is the approximate distance between points A and B?

What is the approximate distance between points A and B?

A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1. The ordered pair negative 4, 5 is labeled as A, and the ordered pair 3, negative 2 is labeled as B.

A coordinate grid is shown from negative 5 to 0 to 5 on both axes at increments of 1. The ordered pair negative 4, 5 is labeled as A, and the ordered pair 3, negative 2 is labeled as B.

3.74 units

7.95 units

8.56 units

9.90 units

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To determine whether the two lines are parallel when a pair of alternate interior angles are right angles, you can apply the alternate interior angles theorem.

The alternate interior angles theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles formed are congruent.

In this case, if the pair of alternate interior angles are right angles, it means they measure 90 degrees.

So, if you find that the pair of alternate interior angles formed by the two lines cut by the transversal are both right angles (measuring 90 degrees), it implies that the two lines are parallel.

Conversely, if the pair of alternate interior angles are not right angles (i.e., they do not measure 90 degrees), it indicates that the two lines are not parallel.

Therefore, the answer to your question is: Yes, if a pair of alternate interior angles formed by two lines cut by a transversal are right angles, then the two lines are parallel.