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
31°
31 degrees
132°
132 degrees
124°
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°.