Question

4 in the diagram, line c is parallel to line d, and line f intersects lines c and d. use the diagram to fill in the blanks. the value of x is __ because the angles in the diagram are __.

Explanation:

Step1: Identify angle relationship

The angles \(x^\circ\) and \(97^\circ\) are same-side interior angles formed by transversal \(f\) cutting parallel lines \(c\) and \(d\). Same-side interior angles are supplementary, so:
$$x + 97 = 180$$

Step2: Solve for \(x\)

Subtract 97 from both sides:
$$x = 180 - 97$$

Answer:

The value of \(x\) is \(83\)
because the angles in the diagram
are supplementary same-side interior angles.