Question

given ( m parallel n ), find the value of ( x ).
diagram: two parallel lines ( m ) (top) and ( n ) (bottom) with a transversal. angle on ( m ): ( (7x - 17)^circ ), angle on ( n ): ( (7x + 1)^circ ).
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \), the two angles \( (7x - 17)^\circ \) and \( (7x + 1)^\circ \) are same - side interior angles? Wait, no, actually, looking at the diagram, these two angles should be supplementary? Wait, no, wait. Wait, when two parallel lines are cut by a transversal, same - side interior angles are supplementary. Wait, but let's check the positions. Wait, the angle \( (7x - 17)^\circ \) and the angle \( (7x + 1)^\circ \): Wait, maybe they are alternate exterior or something? Wait, no, actually, if we consider the vertical angles and the parallel lines, maybe these two angles are supplementary? Wait, no, let's think again. Wait, when \( m\parallel n \), and the transversal cuts them, the angle \( (7x - 17)^\circ \) and \( (7x + 1)^\circ \): Wait, maybe I made a mistake. Wait, actually, if we look at the diagram, the two angles \( (7x - 17)^\circ \) and \( (7x + 1)^\circ \) are same - side interior angles? No, wait, same - side interior angles add up to \( 180^\circ \). Wait, let's set up the equation: \( (7x - 17)+(7x + 1)=180 \)? Wait, no, that can't be. Wait, maybe they are alternate interior angles? No, alternate interior angles are equal. Wait, maybe the angle \( (7x - 17)^\circ \) and the angle adjacent to \( (7x + 1)^\circ \) are equal. Wait, no, let's re - examine.

Wait, actually, when two parallel lines are cut by a transversal, the consecutive interior angles (same - side interior angles) are supplementary. Wait, maybe the angle \( (7x - 17)^\circ \) and \( (7x + 1)^\circ \) are same - side interior angles. So we have the equation:

\( (7x - 17)+(7x + 1)=180 \)

Step2: Solve the equation

First, combine like terms:

\( 7x+7x-17 + 1=180 \)

\( 14x-16 = 180 \)

Then, add 16 to both sides:

\( 14x=180 + 16 \)

\( 14x=196 \)

Then, divide both sides by 14:

\( x=\frac{196}{14}=14 \)

Answer:

\( x = 14 \)