Question

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

Explanation:

Step1: Use linear - pair property

Since $(6x + 14)^{\circ}$ and $(8x+4)^{\circ}$ form a linear - pair, their sum is $180^{\circ}$. So, $(6x + 14)+(8x + 4)=180$.
Combining like terms, we get $6x+8x+14 + 4=180$, which simplifies to $14x+18 = 180$.
Subtract 18 from both sides: $14x=180 - 18=162$.
Then divide both sides by 14: $x=\frac{162}{14}=\frac{81}{7}=11.5714\approx11.57$.

Step2: Use corresponding - angles property

Since $m\parallel n$, the angle $(2y + 20)^{\circ}$ and $(6x+14)^{\circ}$ are corresponding angles and are equal.
First, find the value of $(6x + 14)$ when $x=\frac{81}{7}$.
$6x+14=6\times\frac{81}{7}+14=\frac{486}{7}+14=\frac{486 + 98}{7}=\frac{584}{7}\approx83.43$.
Then set $2y+20=\frac{584}{7}$.
Subtract 20 from both sides: $2y=\frac{584}{7}-20=\frac{584 - 140}{7}=\frac{444}{7}$.
Divide both sides by 2: $y=\frac{222}{7}\approx31.71$.

Answer:

$x=\frac{81}{7}\approx11.57$, $y = \frac{222}{7}\approx31.71$