Question

give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.
(a) alternate interior angles: ∠4 and ∠6
(b) corresponding angles: ∠1 and ∠5
(c) alternate exterior angles: ∠1 and ∠7

Explanation:

Step1: Recall Angle Definitions

• Alternate Interior Angles: Lie between two lines, on opposite sides of a transversal.
• Corresponding Angles: Occupy the same relative position at each intersection.
• Alternate Exterior Angles: Lie outside two lines, on opposite sides of a transversal.

Step2: Analyze Each Part

(a) Alternate Interior Angles

Lines \( g \) and \( h \), transversal \( a \). Interior angles: \( \angle 3, \angle 4, \angle 5, \angle 6 \). Alternate interior: \( \angle 3 \) & \( \angle 6 \), \( \angle 4 \) & \( \angle 5 \). Given \( \angle 4 \) & \( \angle 6 \) are adjacent, not alternate interior. Incorrect.

(b) Corresponding Angles

\( \angle 1 \) (top-left, \( g \)-\( a \)) and \( \angle 5 \) (top-left, \( h \)-\( a \)): same relative position. Correct.

(c) Alternate Exterior Angles

Exterior angles: \( \angle 1, \angle 2, \angle 7, \angle 8 \). Alternate exterior: \( \angle 1 \) & \( \angle 8 \), \( \angle 2 \) & \( \angle 7 \). Given \( \angle 1 \) & \( \angle 7 \): \( \angle 1 \) is top, \( \angle 7 \) is bottom-left, not alternate exterior. Incorrect.

Answer:

(b) Corresponding angles: \( \angle 1 \) and \( \angle 5 \)