To find the measure of ∠F, we first need to determine the measures of the angles ∠D and ∠E given that they are supplementary. Supplementary angles add up to 180 degrees.
We have:
- \( m∠D = (4x + 8)° \)
- \( m∠E = (x + 17)° \)
Since ∠D and ∠E are supplementary, we can set up the equation: \[ m∠D + m∠E = 180° \]
Plugging in the expressions for m∠D and m∠E: \[ (4x + 8) + (x + 17) = 180 \]
Combining like terms: \[ 5x + 25 = 180 \]
Now, we will solve for \( x \): \[ 5x = 180 - 25 \] \[ 5x = 155 \] \[ x = \frac{155}{5} = 31 \]
Now that we have the value of \( x \), we can find the measure of ∠D: \[ m∠D = 4(31) + 8 = 124° \]
Since ∠F is a vertical angle to ∠D, they are equal in measure: \[ m∠F = m∠D = 124° \]
Therefore, the measure of ∠F is: \[ \boxed{124°} \]
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