Question

classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. 1. \\( \angle 1 \\) and \\( \angle 9 \\) 2. \\( \angle 8 \\) and \\( \angle 13 \\) 3. \\( \angle 6 \\) and \\( \angle 16 \\) 4. \\( \angle 4 \\) and \\( \angle 10 \\) 5. \\( \angle 8 \\) and \\( \angle 16 \\) 6. \\( \angle 10 \\) and \\( \angle 13 \\)

Explanation:

Step1: Recall the definitions

• Corresponding angles: Angles in the same relative position.
• Alternate interior angles: Between the two lines and on opposite sides of the transversal.
• Alternate exterior angles: Outside the two lines and on opposite sides of the transversal.
• Consecutive interior angles: Between the two lines and on the same side of the transversal.

Step2: Analyze each pair

• For \( \angle1 \) and \( \angle9 \): They are in the same relative position (top - left at their respective intersections), so they are corresponding angles.
• For \( \angle8 \) and \( \angle13 \): They are between the two lines (\(x\) and \(y\)) and on opposite sides of the transversal (\(b\)), so they are alternate interior angles.
• For \( \angle6 \) and \( \angle16 \): They are outside the two lines (\(x\) and \(y\)) and on opposite sides of the transversal (\(b\)), so they are alternate exterior angles.
• For \( \angle4 \) and \( \angle10 \): They are in the same relative position (bottom - left at their respective intersections), so they are corresponding angles.
• For \( \angle8 \) and \( \angle16 \): They are in the same relative position (bottom - right at their respective intersections), so they are corresponding angles.
• For \( \angle10 \) and \( \angle13 \): They are between the two lines (\(x\) and \(y\)) and on the same side of the transversal (\(b\)), so they are consecutive interior angles.

Answer:

1. Corresponding angles
2. Alternate interior angles
3. Alternate exterior angles
4. Corresponding angles
5. Corresponding angles
6. Consecutive interior angles