Question

8 find the value of x so that ( l parallel m ). state the converse used. ((4x + 7)^circ) ((6x - 63)^circ) ( l ) ( m ) ( x = 35 ) converse corresponding angles

Explanation:

Step1: Identify the relationship

Since \( l \parallel m \), the two angles \( (4x + 7)^\circ \) and \( (6x - 63)^\circ \) are corresponding angles. By the Converse of Corresponding Angles Theorem, corresponding angles are equal when lines are parallel. So we set the two expressions equal:
\( 4x + 7 = 6x - 63 \)

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides:
\( 7 = 2x - 63 \)
Add 63 to both sides:
\( 7 + 63 = 2x \)
\( 70 = 2x \)
Divide both sides by 2:
\( x = \frac{70}{2} = 35 \)

Answer:

\( x = 35 \), and the converse used is the Converse of Corresponding Angles Theorem (stating that if corresponding angles are congruent, then the lines are parallel).