Question

given m || n, find the value of x and y.

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, we have $5x - 1=4x + 6$.

Step2: Solve for $x$

Subtract $4x$ from both sides of the equation $5x - 1=4x + 6$.
$5x-4x-1=4x - 4x+6$, which simplifies to $x - 1=6$. Then add 1 to both sides: $x=6 + 1=7$.

Step3: Find the value of $y$

The angles $(5x - 1)^{\circ}$ and $y^{\circ}$ are supplementary (linear - pair of angles), so $(5x - 1)+y = 180$. Substitute $x = 7$ into the equation. First, find the value of $5x-1$: $5\times7-1=35 - 1=34$. Then, $34+y = 180$. Subtract 34 from both sides: $y=180 - 34 = 146$.

Answer:

$x = 7$, $y = 146$