To find the measure of angle \( \angle F \), we first need to determine the measures of the angles \( \angle D \) and \( \angle E \). Since \( \angle D \) and \( \angle E \) are supplementary angles, their measures add up to 180°.
Given:
- \( m\angle D = (4x + 8)° \)
- \( m\angle E = (x + 17)° \)
Setting up the equation: \[ (4x + 8) + (x + 17) = 180 \] Combining like terms: \[ 5x + 25 = 180 \] Subtracting 25 from both sides: \[ 5x = 155 \] Dividing by 5: \[ x = 31 \]
Now substitute \( x \) back into the expression for \( m\angle D \): \[ m\angle D = 4(31) + 8 = 124 + 8 = 132° \]
Since \( \angle F \) is a vertical angle to \( \angle D \), it has the same measure as \( \angle D \): \[ m\angle F = m\angle D = 132° \]
Therefore, the measure of \( \angle F \) is 132°.
Final Answer: 132°
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