Since lines \( m \) and \( n \) are parallel, and angles \( E \) and \( B \) are corresponding angles, they are equal. We can set up the equation:
\[ 3x + 18 = 14x - 8 \]
To solve for \( x \), first, we'll rearrange the equation to get all terms involving \( x \) on one side and constant terms on the other:
- Subtract \( 3x \) from both sides:
\[ 18 = 14x - 3x - 8 \]
This simplifies to:
\[ 18 = 11x - 8 \]
- Next, add 8 to both sides:
\[ 18 + 8 = 11x \]
This simplifies to:
\[ 26 = 11x \]
- Now, divide both sides by 11:
\[ x = \frac{26}{11} \]
To convert this to a decimal, you can divide:
\[ x \approx 2.36 \]
None of the given response options (48, 132, 10, 2611) matches the calculated value of \( x \). It's possible that there was a misinterpretation of the angles or parallel lines' properties.
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1 answer