Question

find the value of the variable if ( mparallel l ).
( mangle4 = 12x - 1 ) and ( mangle5 = 8x + 27 )
the diagram is not to scale.

Explanation:

Step1: Use the property of alternate interior angles

Since \(m\parallel l\), \(\angle4\) and \(\angle5\) are alternate interior angles. So \(m\angle4 = m\angle5\).
$$12x - 1=8x + 27$$

Step2: Solve the equation for \(x\)

Subtract \(8x\) from both sides:
$$12x-8x - 1=8x-8x + 27$$
$$4x-1 = 27$$
Add \(1\) to both sides:
$$4x-1 + 1=27 + 1$$
$$4x=28$$
Divide both sides by \(4\):
$$x=\frac{28}{4}$$

Answer:

\(x = 7\)