Question

given m || n, find the value of x and y.
(9x + 2)°
(3x - 14)°
y°
m
n

Explanation:

Step1: Use linear - pair property

Since $(9x + 2)^{\circ}$ and $(3x-14)^{\circ}$ are a linear - pair, their sum is $180^{\circ}$. So, $(9x + 2)+(3x - 14)=180$.

Step2: Simplify the equation

Combine like terms: $9x+3x+2 - 14 = 180$, which gives $12x-12 = 180$.

Step3: Solve for $x$

Add 12 to both sides of the equation: $12x=180 + 12=192$. Then divide both sides by 12, so $x=\frac{192}{12}=16$.

Step4: Find the value of $y$

Since $(3x - 14)^{\circ}$ and $y^{\circ}$ are vertical angles, they are equal. Substitute $x = 16$ into $3x-14$: $3\times16-14=48 - 14 = 34$. So $y = 34$.

Answer:

$x = 16$, $y = 34$