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

132°
132 degrees

31°
31 degrees

48°
48 degrees

124°
124 degrees

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measure of angle ∠F, we need to understand that vertical angles are always congruent. Therefore, ∠D = ∠F and we can equate their measures:

m∠D = m∠F
4x + 8 = x + 17

Now, let's solve for x:
3x = 9
x = 3

Substitute the value of x back into the equation for ∠F:
m∠F = 4x + 8 = 4(3) + 8 = 12 + 8 = 20

Therefore, the measure of angle ∠F is 20 degrees.

Answer 2

thatas not an answer choice

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the confusion. Since ∠D and ∠E are supplementary angles, we know that their measures add up to 180 degrees:

m∠D + m∠E = 180

Substituting the given measures:

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

Combining like terms:

5x + 25 = 180

Subtracting 25 from both sides:

5x = 155

Dividing both sides by 5:

x = 31

Now, we can find the measure of ∠F by substituting the value of x into the measure of ∠D:

m∠F = 4x + 8 = 4(31) + 8 = 124 + 8 = 132

Therefore, the measure of ∠F is 132 degrees. The correct answer choice is:

132°