If there are two supplementary angles, ∠D

Question

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

31°
31 degrees

132°
132 degrees

124°

Answer 1

To find the measure of ∠F, we need to determine the value of x. Since ∠D and ∠E are supplementary angles, their measures add up to 180 degrees:

m∠D + m∠E = 180°

(4x + 8) + (x + 17) = 180

5x + 25 = 180

5x = 155

x = 31

Now that we know x = 31, we can substitute it back into the expression for ∠D to find its measure:

m∠D = (4x + 8)°

m∠D = (4(31) + 8)°

m∠D = 124°

Since ∠F is a vertical angle with ∠D, it has the same measure. Therefore, the measure of ∠F is 124°.

Therefore, the correct answer is 124°.