Question

a transversal intersecting two lines creates eight different angles: ____ pairs of corresponding angles, __ pairs of alternate interior angles, and ____ pairs of alternate exterior angles.
a. 2...2...2
b. 4...2...2
c. 2...2...4
d. 4...4...4
please select the best answer from the choices provided
○ a
○ b
○ c
○ d

Explanation:

• Corresponding angles: When a transversal intersects two lines, corresponding angles are in the same relative position. There are 4 pairs of corresponding angles. For example, if we label the angles formed by the transversal and the two lines as \( \angle1,\angle2,\angle3,\angle4,\angle5,\angle6,\angle7,\angle8\), then \((\angle1,\angle5)\), \((\angle2,\angle6)\), \((\angle3,\angle7)\), \((\angle4,\angle8)\) are the pairs of corresponding angles.
• Alternate - interior angles: Alternate - interior angles are between the two lines and on opposite sides of the transversal. There are 2 pairs of alternate - interior angles. The pairs are \((\angle3,\angle6)\) and \((\angle4,\angle5)\).
• Alternate - exterior angles: Alternate - exterior angles are outside the two lines and on opposite sides of the transversal. There are 2 pairs of alternate - exterior angles. The pairs are \((\angle1,\angle8)\) and \((\angle2,\angle7)\).

Answer:

B. 4...2...2