Question

1. if ( mangle1 = 3x - 3 ) and ( mangle5 = 7x + 23 ), for what value of ( x ) is ( ellparallel m )?

Explanation:

Step1: Use the property of parallel lines

When \( \ell\parallel m\), \( \angle1\) and \( \angle5\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So, \(m\angle1 = m\angle5\).

Step2: Set up the equation

Set \(3x - 3=7x + 23\).

Step3: Solve the equation for \(x\)

Subtract \(3x\) from both sides:
\(3x-3 - 3x=7x + 23-3x\)
\(-3 = 4x+23\)
Subtract \(23\) from both sides:
\(-3-23=4x + 23-23\)
\(-26 = 4x\)
Divide both sides by \(4\):
\(x=\frac{-26}{4}=-\frac{13}{2}=-6.5\)

Answer:

\(x = - 6.5\)