Question

given ( m parallel n ), find the value of ( x ).

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \) and \( t \) is a transversal, the \( 38^\circ \) angle and \( x^\circ \) are supplementary (linear pair) or vertical? Wait, no, looking at the diagram, the \( 38^\circ \) and \( x \) are adjacent and form a linear pair? Wait, no, actually, when two lines are parallel and cut by a transversal, the consecutive interior angles? Wait, no, the \( 38^\circ \) and \( x \) are supplementary because they form a linear pair (they are adjacent and on a straight line). Wait, no, linear pair sums to \( 180^\circ \)? Wait, no, wait, the angle of \( 38^\circ \) and \( x \) are supplementary? Wait, no, actually, the \( 38^\circ \) and \( x \) are adjacent and form a linear pair, so \( 38 + x = 180 \)? Wait, no, wait, maybe vertical angles? Wait, no, let's re-examine. The two lines \( m \) and \( n \) are parallel, cut by transversal \( t \). The angle of \( 38^\circ \) and \( x \) are supplementary because they are same - side interior? No, wait, the diagram: the \( 38^\circ \) and \( x \) are adjacent, forming a linear pair, so they should be supplementary. Wait, no, linear pair is two angles that are adjacent and their non - common sides form a straight line. So if one angle is \( 38^\circ \), the other \( x \) should satisfy \( 38 + x = 180 \)? Wait, no, wait, maybe I made a mistake. Wait, actually, the \( 38^\circ \) and \( x \) are supplementary? Wait, no, let's think again. The angle of \( 38^\circ \) and \( x \) are adjacent, so they form a linear pair, so \( x = 180 - 38 \)? Wait, no, wait, maybe they are vertical angles? No, vertical angles are equal. Wait, no, the \( 38^\circ \) and \( x \) are supplementary. Wait, let's calculate: if \( 38 + x = 180 \), then \( x = 180 - 38=142 \)? Wait, no, that can't be. Wait, maybe the \( 38^\circ \) and \( x \) are supplementary? Wait, no, maybe I misread the diagram. Wait, the two lines \( m \) and \( n \) are parallel, and the transversal \( t \) cuts them. The angle of \( 38^\circ \) and \( x \) are adjacent, so they are supplementary. So \( x = 180 - 38 = 142 \)? Wait, no, wait, maybe the \( 38^\circ \) and \( x \) are supplementary. Wait, let's do the calculation:

Step2: Calculate \( x \)

Since the two angles \( 38^\circ \) and \( x^\circ \) form a linear pair (they are adjacent and their non - common sides form a straight line), we know that the sum of angles in a linear pair is \( 180^\circ \). So we have the equation:
\( 38 + x=180 \)
To solve for \( x \), we subtract \( 38 \) from both sides of the equation:
\( x = 180 - 38 \)
\( x = 142 \)

Answer:

\( x = 142 \)