given ( m parallel n ), find the value of ( x ). \nanswer attempt 1 out of 2 \n( x = )

Explanation:

Step1: Identify angle relationship

Since ( m \parallel n ), the two angles ( (8x - 1)^\circ ) and ( (9x - 11)^\circ ) are same - side interior angles? Wait, no, actually, looking at the diagram, they are supplementary? Wait, no, when two parallel lines are cut by a transversal, same - side interior angles are supplementary, but also, these two angles look like they are adjacent and form a linear pair? Wait, no, the two angles ( (8x - 1)^\circ ) and ( (9x - 11)^\circ ) are actually alternate interior angles? Wait, no, let's re - examine. Wait, the two angles ( (8x - 1)^\circ ) and ( (9x - 11)^\circ ): since ( m\parallel n ), and the transversal is the horizontal line. Wait, actually, the two angles ( (8x - 1)^\circ ) and ( (9x - 11)^\circ ) are supplementary? No, wait, no. Wait, when two parallel lines are cut by a transversal, consecutive interior angles are supplementary, but also, if we look at the vertical angles or alternate interior angles. Wait, no, the two angles ( (8x - 1)^\circ ) and ( (9x - 11)^\circ ) are actually equal? Wait, no, that can't be. Wait, maybe they are same - side interior angles? Wait, no, let's think again. Wait, the correct relationship: when two parallel lines are cut by a transversal, the same - side interior angles are supplementary. But in this case, the two angles ( (8x - 1)^\circ ) and ( (9x - 11)^\circ ) are actually supplementary? Wait, no, wait, the sum of same - side interior angles is ( 180^\circ ). Wait, no, maybe I made a mistake. Wait, looking at the diagram, the two angles ( (8x - 1)^\circ ) and ( (9x - 11)^\circ ) are adjacent and form a linear pair? No, they are on the same side of the transversal. Wait, actually, the correct relationship is that ( (8x - 1)+(9x - 11)=180 )? No, that would be if they are same - side interior angles. Wait, no, wait, maybe they are alternate interior angles? Wait, no, alternate interior angles are equal. Wait, let's check the diagram again. The two angles ( (8x - 1)^\circ ) and ( (9x - 11)^\circ ): since ( m\parallel n ), and the transversal is the horizontal line, the two angles are actually equal? Wait, no, that doesn't make sense. Wait, maybe I got the angle types wrong. Wait, let's start over.

When two parallel lines are cut by a transversal, alternate interior angles are equal. Let's see, the angle ( (8x - 1)^\circ ) and the angle ( (9x - 11)^\circ ): if we consider the transversal, maybe they are alternate interior angles. So we set ( 8x-1 = 9x - 11 ).

Step2: Solve for x

Start with the equation ( 8x-1=9x - 11 ).

Subtract ( 8x ) from both sides: ( 8x-1 - 8x=9x - 11-8x ), which simplifies to ( - 1=x - 11 ).

Then add 11 to both sides: ( -1 + 11=x-11 + 11 ), so ( x = 10 ).

Wait, let's check. If ( x = 10 ), then ( 8x-1=8\times10 - 1=79 ), and ( 9x - 11=9\times10-11 = 79 ). So they are equal, which means they are alternate interior angles, so that makes sense because ( m\parallel n ), alternate interior angles are equal.

Answer:

( x = 10 )