Question

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

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, we have $3x - 19=2x + 1$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $3x-2x-19=2x - 2x+1$, which simplifies to $x-19 = 1$. Then add 19 to both sides: $x=1 + 19$, so $x = 20$.

Step3: Use corresponding - angle property

Since $m\parallel n$, corresponding angles are equal. Let's assume $(5y + 19)^{\circ}$ and $(3x-19)^{\circ}$ are corresponding angles. Substitute $x = 20$ into $(3x-19)$: $3\times20-19=60 - 19=41$. So $5y+19 = 41$.

Step4: Solve for $y$

Subtract 19 from both sides: $5y+19-19=41 - 19$, which gives $5y=22$. Then divide both sides by 5: $y=\frac{22}{5}=4.4$.

Answer:

$x = 20$, $y = 4.4$