Question

1. in each diagram, line p is parallel to line f, and line t intersects lines p and f.

Explanation:

Step1: Identify the angle relationship

Since line \( p \) is parallel to line \( f \), and line \( t \) is a transversal, the corresponding angles are equal. The angle of \( 75^\circ \) on line \( p \) and the angle \( x^\circ \) on line \( f \) are corresponding angles.

Step2: Apply the corresponding angles postulate

By the corresponding angles postulate (when two parallel lines are cut by a transversal, corresponding angles are congruent), we have \( x = 75 \).

Answer:

\( x = 75 \)