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transversals of parallel lines: find angle measures
lesson: transversals of parallel lines

Explanation:

Step1: Identify angle relationship

The two angles \((x + 120)^\circ\) and \((9x)^\circ\) are same - side interior angles formed by a transversal intersecting two parallel lines. Same - side interior angles are supplementary, meaning their sum is \(180^\circ\). So we can set up the equation: \((x + 120)+9x=180\).

Step2: Simplify the equation

Combine like terms on the left - hand side of the equation. \(x+9x + 120=180\), which simplifies to \(10x+120 = 180\).

Step3: Solve for x

Subtract 120 from both sides of the equation: \(10x+120 - 120=180 - 120\), so \(10x=60\). Then divide both sides by 10: \(\frac{10x}{10}=\frac{60}{10}\), which gives \(x = 6\).

Answer:

\(x = 6\)