Question

skill set #3 - angle relationships with parallel lines
given m || n, find the value of x.
(6x + 9)°
(4x + 15)°

Explanation:

Step1: Use the property of parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So, \((6x + 9)+(48 + 15)=180\).

Step2: Simplify the equation

First, calculate \(48 + 15 = 63\). Then the equation becomes \(6x+9 + 63=180\), which simplifies to \(6x+72 = 180\).

Step3: Solve for \(x\)

Subtract \(72\) from both sides: \(6x=180 - 72\), so \(6x = 108\). Divide both sides by \(6\): \(x=\frac{108}{6}\).

Answer:

\(x = 18\)