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

124°
124 degrees

31°
31 degrees

48°

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°. Therefore, we can set up the equation:

m∠D + m∠E = 180

(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 that we have the value of x, we can substitute it back into the equation for ∠D:

m∠D = (4x + 8)°
m∠D = (4(31) + 8)°
m∠D = 132°

Since ∠F is a vertical angle with ∠D, the measure of ∠F is also 132°.

Therefore, the correct answer is:

132°