Question

check design find the values of x and y such that pr and qs are perpendicular. x = y =

Explanation:

Step1: Recall perpendicular - angle property

Since $\overline{PR}$ and $\overline{QS}$ are perpendicular, the angle at their intersection is $90^{\circ}$. So, we have the equation $2x+(5x + 6)=90$.

Step2: Solve the equation for $x$

Combine like - terms: $2x+5x+6 = 90$, which simplifies to $7x+6 = 90$. Subtract 6 from both sides: $7x=90 - 6=84$. Then divide both sides by 7: $x=\frac{84}{7}=12$.

Step3: Use the right - angle property for the other angle

The angle $\angle PQR = 90^{\circ}$, so $4y-2+2x = 90$. Substitute $x = 12$ into the equation: $4y-2+2\times12 = 90$.

Step4: Simplify and solve for $y$

First, simplify the left - hand side: $4y-2 + 24=90$, which is $4y+22 = 90$. Subtract 22 from both sides: $4y=90 - 22 = 68$. Divide both sides by 4: $y=\frac{68}{4}=17$.

Answer:

$x = 12$, $y = 17$