Question

7 find the value of x so that ( l parallel m ). state the converse used.
(26x - 4)° ( l )
( m )
(15x + 29)°
( x = )
converse

Explanation:

Step1: Identify the relationship

The angles \((26x - 4)^\circ\) and \((15x + 29)^\circ\) are alternate exterior angles. For lines \(l\) and \(m\) to be parallel, alternate exterior angles must be equal (Converse of Alternate Exterior Angles Theorem). So we set up the equation:
\(26x - 4 = 15x + 29\)

Step2: Solve for \(x\)

Subtract \(15x\) from both sides:
\(26x - 15x - 4 = 15x - 15x + 29\)
\(11x - 4 = 29\)

Add 4 to both sides:
\(11x - 4 + 4 = 29 + 4\)
\(11x = 33\)

Divide both sides by 11:
\(x=\frac{33}{11}\)
\(x = 3\)

Answer:

\(x = 3\)
converse: Converse of Alternate Exterior Angles Theorem (If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel)