Question

given m∥n, find the value of x.
(2x-4)°
(3x-12)°
answer attempt 1 out of 2
x =
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Explanation:

Step1: Identify angle relationship

Since \( m \parallel n \) and \( t \) is a transversal, the angles \( (2x - 4)^\circ \) and \( (3x - 12)^\circ \) are corresponding angles (or alternate exterior angles, depending on the position), so they are equal. Thus, we set up the equation:
\( 2x - 4 = 3x - 12 \)

Step2: Solve for \( x \)

Subtract \( 2x \) from both sides:
\( -4 = x - 12 \)
Add 12 to both sides:
\( x = -4 + 12 \)
\( x = 8 \)

Wait, no, wait. Wait, maybe I made a mistake in angle relationship. Wait, actually, looking at the diagram, maybe they are alternate interior or corresponding? Wait, no, let's re-examine. Wait, the angle \( (2x - 4)^\circ \) and \( (3x - 12)^\circ \) – maybe they are equal because of parallel lines and transversal, so corresponding angles. Wait, but when I solve \( 2x - 4 = 3x - 12 \), we get \( -x = -8 \), so \( x = 8 \)? Wait, no, wait: \( 2x - 4 = 3x - 12 \) → \( -4 + 12 = 3x - 2x \) → \( 8 = x \). Wait, but let's check again. Wait, maybe the angles are equal, so:

Wait, let's do the algebra again. Starting with \( 2x - 4 = 3x - 12 \). Subtract \( 2x \) from both sides: \( -4 = x - 12 \). Then add 12 to both sides: \( x = 8 \). Wait, but let's verify. If \( x = 8 \), then \( 2x - 4 = 12 \), \( 3x - 12 = 12 \). So they are equal, which makes sense for corresponding angles. So that works.

Wait, but maybe I messed up the angle relationship. Let's think again. Since \( m \parallel n \), and \( t \) is a transversal, the angle \( (2x - 4)^\circ \) and \( (3x - 12)^\circ \) – are they corresponding? Let's see the positions. The upper angle on line \( m \) and the lower angle on line \( n \) – maybe alternate exterior or corresponding. Either way, if they are equal, the equation holds. So solving gives \( x = 8 \). Wait, but wait, maybe I made a mistake. Wait, let's check the signs. Wait, \( 2x - 4 = 3x - 12 \) → \( 3x - 2x = 12 - 4 \) → \( x = 8 \). Yes, that's correct.

Answer:

\( x = 8 \)