Question

given m || n, find the value of x and y.
(7y - 15)° (x - 14)° m
(2x + 8)° n

Explanation:

Step1: Use corresponding - angles property

Since $m\parallel n$, the corresponding angles are equal. So, $2x + 8=x - 14$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $2x - x+8=x - x - 14$, which gives $x+8=-14$. Then subtract 8 from both sides: $x=-14 - 8=-22$.

Step3: Use linear - pair property

The angles $(7y - 15)^{\circ}$ and $(x - 14)^{\circ}$ form a linear - pair. Since $x=-22$, then $(x - 14)^{\circ}=(-22 - 14)^{\circ}=-36^{\circ}$ (but we use the non - negative angle measure concept for angles in geometry, and the linear - pair relationship gives $7y-15+(x - 14)=180$). Substitute $x = - 22$ into the equation: $7y-15+(-22 - 14)=180$.
$7y-15-36 = 180$.
$7y-51 = 180$.
Add 51 to both sides: $7y=180 + 51=231$.
Divide both sides by 7: $y=\frac{231}{7}=33$.

Answer:

$x=-22,y = 33$