In a pair of vertical angles, the measures of the angles are equal. Therefore, we can set m∠1 equal to m∠3 to find the value of \(x\):
\[ m∠1 = m∠3 \]
Given: \[ m∠1 = (4x + 26)^\circ \] \[ m∠3 = 98^\circ \]
Now, set them equal to each other: \[ 4x + 26 = 98 \]
Next, solve for \(x\). First, subtract 26 from both sides: \[ 4x = 98 - 26 \] \[ 4x = 72 \]
Now, divide both sides by 4: \[ x = \frac{72}{4} \] \[ x = 18 \]
So the value of \(x\) is 18.