Question

given lines m and n cut by transversal t, match each of the following pairs of angles with the correct relationship. if no relationship, select none.
<1 and <5
<2 and <8
<3 and <6
<2 and <5
<4 and <6

Explanation:

Step1: Recall angle - pair definitions

• Corresponding angles: Angles in the same relative position. For example, if two parallel lines are cut by a transversal, \(\angle1\) and \(\angle5\) are in the upper - left position relative to their intersection points with the transversal.
• Alternate exterior angles: Angles outside the two lines and on opposite sides of the transversal. \(\angle2\) is outside the two lines \(m\) and \(n\) (assuming \(m\parallel n\)), and \(\angle8\) is also outside, and they are on opposite sides of the transversal \(t\). But \(\angle2\) and \(\angle8\) do not have a standard angle - pair relationship (they are not congruent in the general case of two lines cut by a transversal, unless \(m\parallel n\) and we use other angle - chasing, but by definition, they are not a named pair).
• Alternate interior angles: Angles between the two lines and on opposite sides of the transversal. \(\angle3\) and \(\angle6\) are between lines \(m\) and \(n\) and on opposite sides of transversal \(t\).
• \(\angle2\) and \(\angle5\): \(\angle2\) is above line \(m\) and \(\angle5\) is below line \(m\) but above line \(n\). They do not fit the definitions of corresponding, alternate interior, alternate exterior, or consecutive interior/exterior angles.
• Consecutive interior angles: Angles between the two lines and on the same side of the transversal. \(\angle4\) and \(\angle6\) are between lines \(m\) and \(n\) and on the same side of transversal \(t\).

Answer:

\(\angle1\) and \(\angle5\): Corresponding Angles
\(\angle2\) and \(\angle8\): None
\(\angle3\) and \(\angle6\): Alternate Interior Angles
\(\angle2\) and \(\angle5\): None
\(\angle4\) and \(\angle6\): Consecutive Interior Angles