Question

which angle pair does not belong with the other three?
2
by three lines intersecting in one point
by four lines intersecting in one point
by a transversal intersecting two coplanar lines at different points
as alternate exterior angles
explain
they ar
formed

Explanation:

Step1: Recall angle - pair definitions

• Adjacent angles: Angles that have a common side and a common vertex (corner point) and do not overlap. \(\angle2\) and \(\angle3\) are adjacent angles.
• Alternate - interior angles: When a transversal intersects two coplanar lines, alternate - interior angles are non - adjacent interior angles that lie on opposite sides of the transversal. \(\angle4\) and \(\angle5\) are alternate - interior angles.
• Alternate - exterior angles: When a transversal intersects two coplanar lines, alternate - exterior angles are non - adjacent exterior angles that lie on opposite sides of the transversal. \(\angle1\) and \(\angle8\) are alternate - exterior angles, and \(\angle2\) and \(\angle7\) are alternate - exterior angles.

Step2: Compare the angle - pair types

The pair \(\angle2\) and \(\angle3\) is an adjacent - angle pair, while \(\angle4\) and \(\angle5\), \(\angle1\) and \(\angle8\), \(\angle2\) and \(\angle7\) are all non - adjacent angle pairs formed by a transversal intersecting two coplanar lines.

Answer:

\(\angle2\) and \(\angle3\)