To find the value of \( x \), we start by recognizing that vertical angles are equal. Given that \( \angle 1 \) and \( \angle 3 \) are vertical angles, we set their measures equal to each other:
\[ m\angle 1 = m\angle 3 \]
Substituting the given expressions:
\[ 4x + 26 = 98 \]
Now, we can solve for \( x \):
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Subtract 26 from both sides: \[ 4x = 98 - 26 \] \[ 4x = 72 \]
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Divide by 4: \[ x = \frac{72}{4} \] \[ x = 18 \]
Thus, the value of \( x \) is \( 18 \). The correct answer is:
18