Question: Given $m \parallel n$, find the value of $x$. [Diagram description: Two parallel lines, $m$ and…

Given $m \parallel n$, find the value of $x$.

[Diagram description: Two parallel lines, $m$ and $n$, are intersected by a transversal line. The angle between the transversal and line $n$ is $142^\circ$. The angle between the transversal and line $m$ is labeled as $x^\circ$.]

Solution

To find the value of \( x \), we need to use the fact that the lines \( m \) and \( n \) are parallel. The angles marked \( x^\circ \) and \( 142^\circ \) are consecutive interior angles, which means they are supplementary. This gives us the equation: \[ x + 142 = 180 \] Subtract 142 from both sides to solve for \( x \): \[ x = 180 - 142 \] Calculate: \[ x = 38 Given that the lines \(m\) and \(n\) are parallel, we need to find the value of \(x\). The angle of \(x^\circ\) and the angle of \(142^\circ\) are consecutive interior angles, which means they are supplementary. This means that: \[ x + 142 = 180 \] Subtract 142 from both sides to solve for \(x\): \[ x = 180 - 142 \] \[ x = 38 \] So, the value of \(x\) is \(38^\circ\).