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 degrees 31° 31 degrees 124°
The measure of ∠D is given by m∠D=(4x+8)°. Since ∠F is a vertical angle with ∠D, ∠D and ∠F are congruent angles, so ∠F has the same measure as ∠D. Therefore, the measure of ∠F is (4x+8)°.
wrong
Apologies for the incorrect response. Since ∠D and ∠E are supplementary angles, their sum is equal to 180°.
m∠D + m∠E = 180°
(4x + 8) + (x + 17) = 180
5x + 25 = 180
5x = 155
x = 31
Substituting this value back into the expression for ∠D, we can find the measure of ∠D.
m∠D = (4(31) + 8)° = 132°
Since ∠F is a vertical angle with ∠D, ∠F also has a measure of 132°.
Therefore, the correct answer is ∠F = 132°.