To find the measure of angle \( \angle F \), we first need to find the measures of angles \( \angle D \) and \( \angle E \) since they are supplementary angles. This means that their measures add up to \( 180^\circ \).
Given:
- \( m\angle D = (4x + 8)^\circ \)
- \( m\angle E = (x + 17)^\circ \)
Since \( \angle D \) and \( \angle E \) are supplementary, we can set up the equation:
\[ m\angle D + m\angle E = 180^\circ \]
Substituting the expressions for \( m\angle D \) and \( m\angle E \):
\[ (4x + 8) + (x + 17) = 180 \]
Combine like terms:
\[ 5x + 25 = 180 \]
Next, subtract 25 from both sides:
\[ 5x = 155 \]
Now, divide by 5:
\[ x = 31 \]
Now that we have the value of \( x \), we can find \( m\angle D \):
\[ m\angle D = 4x + 8 = 4(31) + 8 = 124 + 8 = 132^\circ \]
Since \( \angle F \) is a vertical angle to \( \angle D \), \( m\angle F \) is equal to \( m\angle D \):
\[ m\angle F = 132^\circ \]
Thus, the measure of \( \angle F \) is \( 132^\circ \). The correct response is:
132°.