Question

if there are two supplementary angles angle, D and angle E where M angle D(4X +8) degrees and M angle E equals(X +17) degrees and angle elf is a vertical angle with an angle D what is the measure of angle F?
48°
132°
124°
31°

Answer 1

To find the measure of angle F, we first need to determine the measures of angles D and E using the information given about supplementary angles.

1. Since angles D and E are supplementary, their measures add up to 180 degrees. Therefore, we can set up the equation:

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

Substituting the values we have:

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

2. Now, we can combine like terms:

\[
4X + X + 8 + 17 = 180
\]

\[
5X + 25 = 180
\]

3. Next, we isolate the variable X:

\[
5X = 180 - 25
\]

\[
5X = 155
\]

\[
X = \frac{155}{5}
\]

\[
X = 31
\]

4. Now we can find the measure of angle D:

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

5. We can also find the measure of angle E:

\[
M \angle E = X + 17 = 31 + 17 = 48^\circ
\]

Since angle F is a vertical angle to angle D, it will have the same measure:

\[
M \angle F = M \angle D = 132^\circ
\]

Thus, the measure of angle F is:

\[
\boxed{132^\circ}
\]