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 31° 31 degrees 48° 48 degrees 124° 124 degrees 132°
To find the measure of angle F, we first need to find the measure of angle D.
Given that angle D and angle E are supplementary, we have:
m∠D + m∠E = 180°
(4x + 8) + (x + 17) = 180
5x + 25 = 180
5x = 155
x = 31
Now, we can find the measure of angle D:
m∠D = 4x + 8
m∠D = 4(31) + 8
m∠D = 124 + 8
m∠D = 132°
Since angle F is a vertical angle with angle D, angle F will also have a measure of 132°.
Therefore, the measure of angle F is 132°.