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. \(x = 7\)