Use the figure to answer the question.
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.
Which angle is an alternate interior angle to angle 5?
Angle 7 is an alternate interior angle to angle 5.
To find the alternate interior angle to angle 5, we need to locate the angle that is on the inside and opposite side of the transversal from angle 5.
In the illustration, angle 5 is formed below the transversal and on the left side of the intersection with upper N. By following the same orientation pattern, the alternate interior angle to angle 5 will be formed on the left side of the intersection with upper M, below the transversal.
Looking at the angles formed around the intersection point of the transversal and upper M, we have angle 3 on the left side below the transversal. Therefore, angle 3 is the alternate interior angle to angle 5.
To find the alternate interior angle to angle 5, we need to understand the concept of alternate interior angles and their relationship to parallel lines and a transversal.
In the given figure, we have two parallel lines, labeled M and N, and a transversal that is right inclined. When a transversal intersects two parallel lines, it creates eight angles: four angles on the top of the transversal and four angles below it.
Alternate interior angles are the pairs of angles that lie on opposite sides of the transversal and are on the inside of the parallel lines. In other words, they are angles that are formed by a pair of parallel lines being crossed by a transversal and are on the inside of the parallel lines, but on opposite sides of the transversal.
In our given figure, angle 5 is formed by the intersection of transversal and line N. To find the alternate interior angle to angle 5, we need to identify an angle that is formed by the intersecting transversal and line M and is on the opposite side of the transversal.
Looking at the figure, we can see that angle 7 is on the opposite side of the transversal and is formed by the intersection of the transversal and line M. Therefore, angle 7 is the alternate interior angle to angle 5.
To summarize:
Angle 7 is the alternate interior angle to angle 5.