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If two angles are supplementary, their measures add up to 180 degrees.
Given that m∠D = (4x+8)° and m∠E = (x+17)°, we can set up the equation:
(4x+8)° + (x+17)° = 180°
Combine like terms:
5x + 25 = 180
Subtract 25 from both sides:
5x = 155
Divide both sides by 5:
x = 31
Substitute this value back into the equation for ∠D:
m∠D = 4(31)+8 = 132°
Since ∠F is a vertical angle with ∠D, ∠F will also have a measure of 132°.