Question

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

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \), the angle \( x^\circ \) and the \( 146^\circ \) angle are same - side interior angles? Wait, no, actually, the angle adjacent to \( 146^\circ \) (let's call it \( y \)) and \( 146^\circ \) are supplementary, so \( y + 146^\circ=180^\circ \), so \( y = 180 - 146=34^\circ \). And \( x \) and \( y \) are corresponding angles (because \( m\parallel n \) and the transversal \( t \)), so \( x=y \).

Step2: Calculate \( x \)

We know that \( x \) and the \( 146^\circ \) angle are supplementary (because they are same - side interior angles? Wait, no, the correct relationship is that \( x \) and the angle supplementary to \( 146^\circ \) are equal (corresponding angles). First, find the supplementary angle of \( 146^\circ \): \( 180 - 146 = 34 \). So \( x = 34 \).

Answer:

34