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transversals of parallel lines: find angle measures (81)

solve linear

lesson: transversals of parallel lines

Explanation:

Step1: Identify angle - relationship

Since $EF\parallel GH$ and $CD$ is a transversal, the angles $(3x + 23)^{\circ}$ and $(5x-1)^{\circ}$ are corresponding angles and are equal. So, $3x + 23=5x - 1$.

Step2: Solve the equation for x

First, subtract $3x$ from both sides of the equation:
$3x+23-3x=5x - 1-3x$, which simplifies to $23 = 2x-1$.
Then, add 1 to both sides: $23 + 1=2x-1 + 1$, giving $24 = 2x$.
Finally, divide both sides by 2: $\frac{24}{2}=\frac{2x}{2}$, so $x = 12$.

Answer:

$12$