Question

which value of y would make $overleftrightarrow{ab}perpoverleftrightarrow{cd}$? (5y - 6)° (5x - 7)° (2y + 5)° (7x - 11)°

Explanation:

Step1: Recall perpendicular - lines property

If $\overleftrightarrow{AB}\perp\overleftrightarrow{CD}$, then the angle between them is $90^{\circ}$. The sum of the angles $(2y + 5)^{\circ}$ and $(5y-6)^{\circ}$ is $90^{\circ}$ (since they form a right - angle).

Step2: Set up the equation

We set up the equation $(2y + 5)+(5y-6)=90$.

Step3: Simplify the left - hand side of the equation

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

Step4: Solve for y

Add 1 to both sides of the equation: $7y-1 + 1=90 + 1$, so $7y=91$. Then divide both sides by 7: $y=\frac{91}{7}=13$.

Answer:

$13$