Question

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transversals of parallel lines: find angle measures (81)

Explanation:

Step1: Identify angle - relationship

Assume lines $RS$ and $TU$ are parallel and $PQ$ is a transversal. The angles $(59 - 2x)^{\circ}$ and $(64 - 3x)^{\circ}$ are corresponding angles. Corresponding angles formed by a transversal intersecting two parallel lines are equal. So, $59 - 2x=64 - 3x$.

Step2: Solve the linear equation

Add $3x$ to both sides of the equation: $59 - 2x+3x=64 - 3x+3x$, which simplifies to $59 + x=64$.

Step3: Isolate $x$

Subtract 59 from both sides: $x=64 - 59$.

Answer:

$x = 5$