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

1. if the ( m angle 1 = 145^{circ} ), then the ( m angle 5 =? )

a. ( 35^{circ} )
b. ( 45^{circ} )
c. ( 135^{circ} )
d. ( 145^{circ} )

Explanation:

Step1: Identify the relationship between ∠2 and ∠6

Since lines \(p\) and \(q\) are parallel, ∠2 and ∠6 are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.

Step2: Determine the measure of ∠6

Given \(m\angle2 = 20^{\circ}\), and because ∠2 and ∠6 are corresponding angles, \(m\angle6=m\angle2\).

Step3: Identify the relationship between ∠7 and ∠6

∠7 and ∠6 are consecutive interior angles. Consecutive interior angles are supplementary (sum to \(180^{\circ}\)) when two parallel lines are cut by a transversal. But this is for question 2's analysis. For question 1, we already found \(m\angle6 = 20^{\circ}\)

Step4: For question 3, identify the relationship between ∠1 and ∠5

∠1 and ∠5 are corresponding angles. Since lines \(p\) and \(q\) are parallel, \(m\angle1=m\angle5\) (corresponding angles property). Given \(m\angle1 = 145^{\circ}\), so \(m\angle5=145^{\circ}\)

Answer:

1. A. \(20^{\circ}\)
2. C. consecutive interior
3. D. \(145^{\circ}\)