If there are two supplementary angles, ∠D and ∠E , where m∠D=(4x+8)° and m∠E=(x+17)°, and ∠F is a vertical angle with ∠D, what is the measure of ∠F? (1 point) Responses 124° 124 degrees 31° 31 degrees 48° 48 degrees 132°
If ∠D and ∠E are supplementary angles, then their measures add up to 180 degrees.
So, (4x+8)° + (x+17)° = 180°
Combining like terms, 5x + 25 = 180
Subtracting 25 from both sides, 5x = 155
Dividing both sides by 5, x = 31
Therefore, m∠E = (31 + 17)° = 48°
Since ∠F is a vertical angle with ∠D, ∠F also has a measure of (4x+8)° = (4*31+8)° = 132°.
The measure of ∠F is 132 degrees. Answer: 132°.