Question

converse used.
2.
converse: ____

Explanation:

Step1: Assume the angles are corresponding

If lines \(a\) and \(b\) are parallel, then the \(74^{\circ}\) angle and \((9x + 11)^{\circ}\) are corresponding angles and are equal.
\[9x+11 = 74\]

Step2: Solve for \(x\)

Subtract 11 from both sides of the equation:
\[9x=74 - 11\]
\[9x = 63\]
Divide both sides by 9:
\[x=\frac{63}{9}=7\]

Step3: State the converse

The converse used is the converse of the corresponding - angles postulate which states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.

Answer:

Converse: If two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. \(x = 7\)