Question

given that the top and bottom sides are parallel, find the value of x. then find the measure of each labeled angle. x = □° (x - 38)°

Explanation:

Step1: Use property of parallel - sided figures

For a figure with top and bottom sides parallel, adjacent angles are supplementary (sum to 180°). So, $(x - 38)+x=180$.

Step2: Combine like - terms

Combining the $x$ terms, we get $x+x-38 = 180$, which simplifies to $2x-38 = 180$.

Step3: Isolate the variable term

Add 38 to both sides of the equation: $2x-38 + 38=180 + 38$, resulting in $2x=218$.

Step4: Solve for $x$

Divide both sides by 2: $\frac{2x}{2}=\frac{218}{2}$, so $x = 109$.

Answer:

$x = 109$