Question

1. identify the alternate interior, consecutive interior, and corresponding angles for \\( \angle 1 \\) by writing the appropriate letter in the correct location in the diagram.

a alternate interior angle
b consecutive interior angle
c corresponding angle

Explanation:

Step1: Recall the definitions

• Alternate interior angles: non - adjacent interior angles on opposite sides of the transversal.
• Consecutive interior angles: adjacent interior angles on the same side of the transversal.
• Corresponding angles: angles in the same relative position.

Step2: Analyze each angle

• For angle \(z\):
• It is in the same relative position as \(\angle1\) with respect to the parallel lines and the transversal. So \(z = C\) (Corresponding Angle).
• For angle \(q\):
• It is on the same side of the transversal and between the two parallel lines (adjacent to \(\angle1\)’s “partner” in the parallel - line - transversal setup). So \(q=B\) (Consecutive Interior Angle).
• For angle \(s\):
• It is non - adjacent and on the opposite side of the transversal between the two parallel lines. So \(s = A\) (Alternate Interior Angle).

Answer:

\(q = B\), \(z = C\), \(s=A\)