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?
Since ∠D and ∠E are supplementary angles, their measures should add up to 180°.
So, we have the equation:
(4x + 8) + (x + 17) = 180
5x + 25 = 180
5x = 180 - 25
5x = 155
x = 155/5
x = 31
Now, we can find the measure of ∠D:
m∠D = 4x + 8
m∠D = 4(31) + 8
m∠D = 124 + 8
m∠D = 132°
Since ∠F is a vertical angle with ∠D, it will have the same measure. Therefore, the measure of ∠F is 132°.