Question

find the value of the variable if ( m parallel l ).
( m angle 3 = 16 + 4 x ) and ( m angle 6 = 6 x )
the diagram is not to scale.

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel l\), \(\angle3\) and \(\angle6\) are alternate interior angles. So \(m\angle3 = m\angle6\).

Step2: Set up the equation

We have \(16 + 4x=6x\).

Step3: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(16+4x - 4x=6x - 4x\), which gives \(16 = 2x\).
Divide both sides by \(2\): \(\frac{16}{2}=\frac{2x}{2}\).

Answer:

\(x = 8\)