An illustration shows a right inclined transversal passing through two parallel lines labeled upper M and upper N. Four angles are formed at the intersections of the transversal with upper M and upper N. The angles formed around the intersection point of the transversal and upper M are labeled clockwise, starting from the upper left quadrant: 1, 2, 4, and 3. The corresponding angles formed around the intersection point of upper N are labeled clockwise, starting from the upper left quadrant: 5, 6, 8, and 7.

Question

Which angle is an alternate interior angle to angle 5?

Answer 1

In the context of parallel lines cut by a transversal, alternate interior angles are pairs of angles that lie between the two lines and are on opposite sides of the transversal.

Given the labeling of angles:

• At the intersection with line \( M \):

  • Top left: angle 1
  • Top right: angle 2
  • Bottom right: angle 3
  • Bottom left: angle 4

• At the intersection with line \( N \):

  • Top left: angle 5
  • Top right: angle 6
  • Bottom right: angle 7
  • Bottom left: angle 8

Since angle 5 is located at the top left of line \( N \), the corresponding alternate interior angle would be the angle that is on the opposite side of the transversal but in the interior of the lines \( M \) and \( N \).

Angle 5 is opposite to angle 4, which is located at the bottom left of line \( M \). Thus, angle 4 is an alternate interior angle to angle 5.