Question

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

Supplementary angles add up to 180°. Therefore, we can set up the equation:

\[
m∠D + m∠E = 180°
\]

Substituting the expressions for the angles:

\[
(4x + 8) + (x + 17) = 180
\]

Combining like terms:

\[
5x + 25 = 180
\]

Next, we can isolate \(x\) by subtracting 25 from both sides:

\[
5x = 155
\]

Now, divide by 5:

\[
x = 31
\]

Now we can find the measure of ∠D:

\[
m∠D = 4x + 8 = 4(31) + 8 = 124 + 8 = 132°
\]

Since ∠F is a vertical angle with ∠D, they are equal in measure. Thus:

\[
m∠F = m∠D = 132°
\]

The final answer is:

132°