Question

lines ( ell ) and ( m ) are intersected by transversal ( t ) and ( ell parallel m ).

why is ( angle 4 cong angle 8 )?

a. ( angle 4 ) and ( angle 8 ) are alternate exterior angles.

b. ( angle 4 ) and ( angle 8 ) are alternate interior angles.

c. ( angle 4 ) and ( angle 8 ) are corresponding angles.

d. ( angle 4 ) and ( angle 8 ) are same - side interior angles.

Explanation:

Step1: Recall angle - pair definitions

• Alternate exterior angles: lie outside the two parallel lines and on opposite sides of the transversal.
• Alternate interior angles: lie between the two parallel lines and on opposite sides of the transversal.
• Corresponding angles: in the same relative position with respect to the parallel lines and the transversal.
• Same - side interior angles: lie between the two parallel lines and on the same side of the transversal.

Step2: Analyze the position of \(\angle4\) and \(\angle8\)

• \(\angle4\) and \(\angle8\) are in the same relative position. When two parallel lines \(l\) and \(m\) are cut by a transversal \(t\), \(\angle4\) and \(\angle8\) occupy the same relative position (lower - right position at their respective intersections of the parallel lines and the transversal).

Answer:

C. \(\angle4\) and \(\angle8\) are corresponding angles.