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 48° 48 degrees 132° 132
Since ∠D and ∠F are vertical angles, they are congruent. Therefore, the measure of ∠F is equal to the measure of ∠D.
Given that m∠D = (4x + 8)°, we can set up the equation:
4x + 8 = x + 17
Subtracting x from both sides gives:
3x + 8 = 17
Subtracting 8 from both sides gives:
3x = 9
Dividing both sides by 3 gives:
x = 3
Substituting x = 3 into the expression for m∠D, we get:
m∠D = (4(3) + 8)°
m∠D = (12 + 8)°
m∠D = 20°
Therefore, the measure of ∠F is 20°.