Question

complete the steps to find the value of x.
118°
4
(8x + 6)°
(8x + 6)° = m∠
(8x + 6)° = °
8x =
x =

Explanation:

Step1: Use vertical angles property

Since the two lines are parallel and cut by a transversal, \((8x + 6)^{\circ}=m\angle4\) (alternate interior angles are equal).

Step2: Find the measure of \(\angle4\)

\(\angle4\) and \(118^{\circ}\) are supplementary. So \(m\angle4 = 180^{\circ}- 118^{\circ}=62^{\circ}\). Then \((8x + 6)^{\circ}=62^{\circ}\).

Step3: Solve for \(8x\)

Subtract \(6\) from both sides: \(8x=62 - 6=56\).

Step4: Solve for \(x\)

Divide both sides by \(8\): \(x=\frac{56}{8}=7\).

Answer:

\((8x + 6)^{\circ}=m\angle\boldsymbol{4}\)；\((8x + 6)^{\circ}=\boldsymbol{62}^{\circ}\)；\(8x=\boldsymbol{56}\)；\(x = \boldsymbol{7}\)