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 angle \( \angle F \), we first need to find the measures of angles \( \angle D \) and \( \angle E \) since they are supplementary angles. This means that their measures add up to \( 180^\circ \).

Given:
- \( m\angle D = (4x + 8)^\circ \)
- \( m\angle E = (x + 17)^\circ \)

Since \( \angle D \) and \( \angle E \) are supplementary, we can set up the equation:

\[
m\angle D + m\angle E = 180^\circ
\]

Substituting the expressions for \( m\angle D \) and \( m\angle E \):

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

Combine like terms:

\[
5x + 25 = 180
\]

Next, subtract 25 from both sides:

\[
5x = 155
\]

Now, divide by 5:

\[
x = 31
\]

Now that we have the value of \( x \), we can find \( m\angle D \):

\[
m\angle D = 4x + 8 = 4(31) + 8 = 124 + 8 = 132^\circ
\]

Since \( \angle F \) is a vertical angle to \( \angle D \), \( m\angle F \) is equal to \( m\angle D \):

\[
m\angle F = 132^\circ
\]

Thus, the measure of \( \angle F \) is \( 132^\circ \). The correct response is:

**132°**.