Question

find the value of the variable if ( mparallel l ).
( mangle 1 = 3x + 41 ) and ( mangle 5 = 5x + 16 )
the diagram is not to scale.
( x = ) type your answer...

Explanation:

Step1: Use the property of parallel lines

When \(m\parallel l\), \(\angle1\) and \(\angle5\) are congruent (corresponding angles). So \(m\angle1 = m\angle5\).

Step2: Set up the equation

Given \(m\angle1=3x + 44\) and \(m\angle5=5x+16\), we have the equation \(3x + 44=5x+16\).

Step3: Solve the equation

Subtract \(3x\) from both sides: \(44 = 2x+16\).
Subtract \(16\) from both sides: \(2x=44 - 16=28\).
Divide both sides by \(2\): \(x=\frac{28}{2}=14\).

Answer:

\(14\)