Question

solve
if ( l parallel m ), and ( mangle 1=(3x + 11)^{circ} ) and ( mangle 2=(5x - 63)^{circ} ), solve for the value of ( x ).

Explanation:

Step1: Use the property of consecutive interior angles

Since \(l\parallel m\), \(\angle1\) and \(\angle2\) are consecutive interior angles. Consecutive interior angles are supplementary, so \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(3x + 11)^{\circ}\) and \(m\angle2=(5x - 63)^{\circ}\) into the equation:
\((3x + 11)+(5x - 63)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(3x+5x+11 - 63=180\)
\(8x-52 = 180\)

Step3: Solve for \(x\)

Add \(52\) to both sides of the equation:
\(8x-52 + 52=180 + 52\)
\(8x=232\)
Divide both sides by \(8\):
\(x=\frac{232}{8}=29\)

Answer:

\(x = 29\)