Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. (overleftrightarrow{ab}) is parallel to (overleftrightarrow{cd}), and (overleftrightarrow{ef}) is perpendicular to (overleftrightarrow{ab}). the number of (90^circ) angles formed by the intersections of (overleftrightarrow{ef}) and the two parallel lines (overleftrightarrow{ab}) and (overleftrightarrow{cd}) is (square)

Explanation:

Step1: Analyze AB and EF

Since \( \overline{EF} \perp \overline{AB} \), the intersection of \( \overline{EF} \) and \( \overline{AB} \) forms 4 right angles (90° angles).

Step2: Analyze AB and CD (AB || CD)

Because \( \overline{AB} \parallel \overline{CD} \) and \( \overline{EF} \perp \overline{AB} \), by the property of parallel lines and a transversal (perpendicular transversal), \( \overline{EF} \) is also perpendicular to \( \overline{CD} \). So the intersection of \( \overline{EF} \) and \( \overline{CD} \) also forms 4 right angles.

Step3: Total 90° angles

Add the number of 90° angles from both intersections: \( 4 + 4 = 8 \).

Answer:

8