Question

use the diagram below to answer the questions to the right. lines p and q are parallel.

1. if ( m angle 2 = 20 ^ { circ } ), then ( m angle 6 =? )

a. ( 20 ^ { circ } )
b. ( 140 ^ { circ } )
c. ( 160 ^ { circ } )
d. ( 40 ^ { circ } )

1. which relationship describes ( angle 7 ) and ( angle 6 )?

a. alternate interior
b. corresponding
c. consecutive interior
d. vertical

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines \(q\) and \(p\) are cut by a transversal, \(\angle2\) and \(\angle6\) are corresponding angles. Corresponding angles are equal when lines are parallel.

Step1: Analyze the relationship between \(\angle7\) and \(\angle6\)

\(\angle7\) and \(\angle6\) are consecutive - interior angles. When two parallel lines \(q\) and \(p\) are cut by a transversal, consecutive - interior angles are supplementary (their sum is \(180^{\circ}\)). But this is not relevant for the first part. For the first part, since \(\angle2\) and \(\angle6\) are corresponding angles (by the definition of corresponding angles: angles in the same relative position with respect to the parallel lines and the transversal), and \(q\parallel p\), we have \(m\angle6=m\angle2\). Given \(m\angle2 = 20^{\circ}\), so \(m\angle6=20^{\circ}\)

Answer:

A. \(20^{\circ}\)