Question

n m||n, find the value of x.
answer attempt 1 out of 2
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Explanation:

Step1: Identify the angle relationship

Since \( m \parallel n \) and the two angles \( (9x - 10)^\circ \) and \( (8x - 14)^\circ \) are alternate interior angles (or corresponding angles, depending on the diagram's exact configuration, but in this case, they should be equal because of parallel lines), we set them equal to each other.

$$ 9x - 10 = 8x - 14 $$

Step2: Solve for \( x \)

Subtract \( 8x \) from both sides:

$$ 9x - 8x - 10 = 8x - 8x - 14 $$

$$ x - 10 = -14 $$

Then add 10 to both sides:

$$ x - 10 + 10 = -14 + 10 $$

$$ x = -4 $$

Wait, that can't be right. Wait, maybe the angles are same - side interior angles? Wait, no, maybe I misidentified the angle relationship. Wait, actually, looking at the diagram again, maybe the angles are alternate exterior or something else? Wait, no, maybe the angles are supplementary? Wait, no, let's re - examine. Wait, if \( m \parallel n \) and the transversal is \( t \), then the angle \( (9x - 10)^\circ \) and the angle adjacent to \( (8x - 14)^\circ \) (vertical angle) might be equal. Wait, no, maybe the two angles are equal as alternate interior angles. Wait, but when I solved \( 9x - 10 = 8x - 14 \), I got \( x=-4 \), which would make the angles negative, which is impossible. So maybe the angles are supplementary? Let's try that. If \( m \parallel n \), then same - side interior angles are supplementary. So \( (9x - 10)+(8x - 14)=180 \)
Combine like terms:

$$ 9x+8x-10 - 14 = 180 $$

$$ 17x-24 = 180 $$

Add 24 to both sides:

$$ 17x=180 + 24 $$

$$ 17x=204 $$

Divide both sides by 17:

$$ x=\frac{204}{17}=12 $$

Ah, I must have misidentified the angle relationship earlier. The correct relationship is that the two angles are same - side interior angles (or consecutive interior angles) and thus supplementary. So the equation should be \( (9x - 10)+(8x - 14)=180 \)

Answer:

\( x = 12 \)