Question

given $m \parallel n$, find the value of $x$.
there is a diagram with two parallel lines $m$ and $n$, and a transversal $t$. the angle formed with line $m$ and transversal $t$ is $(6x - 9)^{circ}$, and the angle formed with line $n$ and transversal $t$ is $(2x - 19)^{circ}$.

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \) and \( t \) is a transversal, the two angles \( (6x - 9)^\circ \) and \( (2x - 19)^\circ \) are same - side interior angles. Same - side interior angles are supplementary, meaning their sum is \( 180^\circ \). So we can set up the equation:
\( (6x - 9)+(2x - 19)=180 \)

Step2: Simplify the left - hand side of the equation

Combine like terms: \( 6x+2x-9 - 19 = 180 \), which simplifies to \( 8x-28 = 180 \)

Step3: Solve for \( x \)

First, add 28 to both sides of the equation: \( 8x-28 + 28=180 + 28 \), so \( 8x=208 \)
Then, divide both sides by 8: \( x=\frac{208}{8}=26 \)

Answer:

\( x = 26 \)