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, $t$. The angle between line $m$ and the transversal is $138^\circ$. The angle between line $n$ and the transversal is $x^\circ$.]

Solution

Given that lines \( m \) and \( n \) are parallel, we need to find the value of \( x \). Since \( m \parallel n \), the corresponding angles are equal. The 138° angle and \( x^\circ \) angle are corresponding angles. So, we set up the equation: \[ x = 138 \] Therefore, \( x = 138 \) degrees.