Question

1. find y if $overline{ad}congoverline{bc}$ and $overline{ab}=30$. a d 8 c y b

Explanation:

Step1: Define segment - length relationship

Since $\overline{AD}\cong\overline{BC}$, let $AD = BC = x$. We know that $AB=AD + DC+CB$. Given $AB = 30$ and $DC = 8$.

Step2: Substitute values into equation

$30=x + 8+x$.

Step3: Simplify the equation

Combine like - terms: $30=2x + 8$.

Step4: Solve for $x$

Subtract 8 from both sides: $2x=30 - 8=22$. Then divide both sides by 2: $x = 11$.

Step5: Find the value of $y$

Since $y=x$, then $y = 11$.

Answer:

11