Question

solve
if ( l parallel m ), and ( mangle1=(3x + 11)^{circ} ) and ( mangle2=(5x - 63)^{circ} ), solve for the value of ( x ).

Explanation:

Step1: Set up the equation

Since \( l\parallel m\), \(\angle1\) and \(\angle2\) are congruent (Alternate Interior Angles Theorem). So \(3x + 11=5x-63\).

Step2: Solve for \(x\)

Subtract \(3x\) from both sides: \(11 = 2x-63\).
Add \(63\) to both sides: \(74=2x\).
Divide both sides by \(2\): \(x = 37\).

Answer:

\(x = 37\)