Question

use the diagram below to identify the given angle pairs.
a. vertical angles
∠2 & ∠3
b. corresponding angles
∠2 & ∠6
c. alternate interior angles
∠2 & ∠7
d. same - side interior angles
∠2 & ∠6
e. supplementary angles
∠2 & ∠3

Explanation:

• Vertical Angles: Vertical angles are opposite angles formed by two intersecting lines. They are equal in measure. In the diagram, there is no pair of vertical angles among the given options.
• Corresponding Angles: Corresponding angles are in the same relative position at each intersection where a straight line crosses two others. ∠2 and ∠6 are corresponding angles.
• Alternate Interior Angles: Alternate interior angles are between the two lines and on opposite sides of the transversal. ∠2 and ∠7 are alternate interior angles.
• Same - Side Interior Angles: Same - side interior angles are between the two lines and on the same side of the transversal. ∠2 and ∠3 are same - side interior angles.
• Supplementary Angles: Supplementary angles add up to 180 degrees. ∠2 and ∠3 are supplementary (if the lines are parallel, same - side interior angles are supplementary).

Answer:

A. Vertical Angles: No pair in the given options.
B. Corresponding Angles: ∠2 & ∠6.
C. Alternate Interior Angles: ∠2 & ∠7.
D. Same - Side Interior Angles: ∠2 & ∠3.
E. Supplementary Angles: ∠2 & ∠3 (if lines are parallel).