Question

which value of y would make $overleftrightarrow{ab} perp overleftrightarrow{cd}$?

Explanation:

Step1: Recall perpendicular - angle property

If $\overleftrightarrow{AB}\perp\overleftrightarrow{CD}$, then $\angle AEC = 90^{\circ}$. So, $(2y + 5)+(5y-6)=90$.

Step2: Combine like - terms

$2y+5y+5 - 6=90$, which simplifies to $7y - 1=90$.

Step3: Solve for y

Add 1 to both sides: $7y=91$. Then divide by 7: $y = 13$.

Answer:

$y = 13$