Question

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

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \), the \( 155^\circ \) angle and \( x^\circ \) are same - side interior angles? No, wait, actually, the \( 155^\circ \) angle and the angle adjacent to \( x \) (on the same line as \( x \)) are supplementary? Wait, no, let's look again. The \( 155^\circ \) angle and \( x \) are same - side interior angles? No, when two parallel lines are cut by a transversal, same - side interior angles are supplementary. Wait, the \( 155^\circ \) angle and \( x \) are same - side interior angles? Wait, no, the angle adjacent to \( 155^\circ \) (let's call it \( y \)) and \( 155^\circ \) are supplementary, so \( y = 180 - 155=25^\circ \). And since \( m\parallel n \), \( x \) and \( y \) are corresponding angles, so \( x = y = 25^\circ \).

Step2: Calculate \( x \)

We know that for two parallel lines \( m \) and \( n \) cut by a transversal, the angle of \( 155^\circ \) and \( x \) (or the angle related to \( x \)): The linear pair with \( 155^\circ \) is \( 180 - 155=25^\circ \). And by the corresponding angles postulate (since \( m\parallel n \)), \( x \) is equal to this \( 25^\circ \) angle. So \( x = 25 \).

Answer:

25