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

124°
124 degrees

48°
48 degrees

132°
132 degrees

31°

Answer 1

To find the measure of angle ∠F, we need to use the fact that ∠D and ∠E are supplementary angles. This means that the sum of their measures is 180 degrees.

So, we can set up the equation:

(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 one of the angle measures to find the measure of ∠D:

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

Since ∠F is a vertical angle with ∠D, it has the same measure:

∠F = 124 degrees

The correct answer is 124°.