Question

given $m\parallel n$, find the value of x.
(4x - 8)°
(7x - 20)°
answer attempt 1 out of 2
$x = $

Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \) and the transversal \( \ell \) intersects them, the alternate interior angles are equal. So \( 4x - 8 = 7x - 20 \).

Step2: Solve for \( x \)

Subtract \( 4x \) from both sides: \( -8 = 3x - 20 \).
Add 20 to both sides: \( 12 = 3x \).
Divide by 3: \( x = 4 \). Wait, no, wait—wait, maybe they are same - side? Wait, no, looking at the diagram, actually, the two angles \( (4x - 8)^\circ \) and \( (7x - 20)^\circ \) are alternate interior angles? Wait, no, maybe I made a mistake. Wait, if \( m \parallel n \), and the transversal cuts them, the two angles given: let's re - examine. Wait, maybe they are equal as alternate interior angles? Wait, no, let's do the equation again. Wait, \( 4x - 8 = 7x - 20 \)
\( - 8+20 = 7x - 4x \)
\( 12 = 3x \)
\( x = 4 \)? Wait, that seems low. Wait, maybe they are supplementary? Wait, no, the diagram: the two angles are on the same side? Wait, no, let's check the positions. If \( m \) and \( n \) are parallel, and the transversal crosses them, the angle \( (4x - 8) \) and \( (7x - 20) \): maybe they are equal (alternate interior). Wait, but when \( x = 4 \), \( 4x - 8=16 - 8 = 8 \), \( 7x - 20 = 28 - 20 = 8 \). Oh, right! So they are equal. So the correct equation is \( 4x - 8 = 7x - 20 \), leading to \( x = 4 \)? Wait, no, wait, \( 7x-4x=20 - 8 \), \( 3x = 12 \), \( x = 4 \). Yes.

Answer:

\( x = 4 \)