Question

problem 10: identify this pair of angles and decide whether the pair is congruent, supplementary, or neither. ∠2 and ∠6 (first taught in lesson 23)

Explanation:

Step1: Identify the type of angles

When a transversal (line \( n \)) intersects two parallel lines (lines \( \ell \) and \( m \)), corresponding angles are in the same relative position at each intersection. $\angle 2$ is at the intersection of line \( n \) and \( \ell \), and $\angle 6$ is at the intersection of line \( n \) and \( m \), so they are corresponding angles.

Step2: Determine congruence/supplementary

By the Corresponding Angles Postulate, if two parallel lines are cut by a transversal, then each pair of corresponding angles is congruent. Since lines \( \ell \) and \( m \) are parallel (implied by the diagram with two parallel horizontal lines and a transversal), $\angle 2$ and $\angle 6$ are congruent. They are not supplementary (their sum is not \( 180^\circ \)) because corresponding angles formed by parallel lines and a transversal are equal, not supplementary (unless they are also right angles, which isn't indicated here).

Answer:

$\angle 2$ and $\angle 6$ are corresponding angles and they are congruent.