Question

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

124°
124 degrees

31°
31 degrees

132°
132 degrees

48°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measure of ∠F, we need to find the value of x first.

Since ∠D and ∠E are supplementary angles, their measures add up to 180 degrees.

So,
m∠D + m∠E = 180
(4x+8) + (x+17) = 180
5x + 25 = 180
5x = 155
x = 31

Now that we have the value of x, we can find the measure of ∠D and ∠E.

m∠D = (4x + 8)°
m∠D = (4*31 + 8)°
m∠D = 124°

m∠E = (x + 17)°
m∠E = (31 + 17)°
m∠E = 48°

Since ∠F is a vertical angle with ∠D, ∠F has the same measure as ∠D.

So, the measure of ∠F is 124°.