Question

the lines c and d are parallel. what is the value of x based on the following angles? draw (-3x + 109)° (x + 67)°

Explanation:

Step1: Use the property of consecutive interior angles

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. So, \((-3x + 109)+(x + 67)=180\).

Step2: Simplify the equation

Combine like - terms: \(-3x+x+109 + 67=180\), which simplifies to \(-2x+176 = 180\).

Step3: Solve for \(x\)

Subtract \(176\) from both sides: \(-2x=180 - 176\), so \(-2x = 4\). Then divide both sides by \(-2\): \(x=\frac{4}{-2}=-2\).

Answer:

\(x=-2\)