Question

give a pair of alternate exterior angles, a pair of corresponding angles, and a pair of alternate interior angles.

(a) alternate exterior angles: \angle \text{ and } \angle
(b) corresponding angles: \angle \text{ and } \angle
(c) alternate interior angles: \angle \text{ and } \angle

Explanation:

⚡ Using what you learned: lines and angles (parallel, transversal, vertical)

Step 1: Identify Alternate Exterior Angles

Alternate exterior angles lie on opposite sides of the transversal line \(b\) and are outside (exterior to) the two lines \(m\) and \(n\).

• Exterior angles: \(\angle 1\), \(\angle 2\), \(\angle 7\), \(\angle 8\)
• Alternate exterior pairs:
• \(\angle 1\) and \(\angle 7\)
• \(\angle 2\) and \(\angle 8\)

We can choose: \(\angle 1\) and \(\angle 7\)

Step 2: Identify Corresponding Angles

Corresponding angles lie in the same relative position at each intersection where the transversal line \(b\) crosses lines \(m\) and \(n\).

• Corresponding pairs:
• \(\angle 2\) (top-left) and \(\angle 6\) (top-left)
• \(\angle 3\) (bottom-left) and \(\angle 5\) (bottom-left)
• \(\angle 1\) (top-right) and \(\angle 7\) (top-right)
• \(\angle 4\) (bottom-right) and \(\angle 8\) (bottom-right)

We can choose: \(\angle 2\) and \(\angle 6\)

Step 3: Identify Alternate Interior Angles

Alternate interior angles lie on opposite sides of the transversal line \(b\) and are inside (interior to) the two lines \(m\) and \(n\).

• Interior angles: \(\angle 3\), \(\angle 4\), \(\angle 5\), \(\angle 6\)
• Alternate interior pairs:
• \(\angle 3\) and \(\angle 5\)
• \(\angle 4\) and \(\angle 6\)

We can choose: \(\angle 3\) and \(\angle 5\)

Answer:

(a) Alternate exterior angles: \(\angle 1\) and \(\angle 7\) (or \(\angle 2\) and \(\angle 8\))

(b) Corresponding angles: \(\angle 2\) and \(\angle 6\) (or \(\angle 3\) and \(\angle 5\), \(\angle 1\) and \(\angle 7\), \(\angle 4\) and \(\angle 8\))

(c) Alternate interior angles: \(\angle 3\) and \(\angle 5\) (or \(\angle 4\) and \(\angle 6\))