Question

If there are two supplementary angles, LD and LE, where m/D = (4x + 8) ° and mLE = (x + 17) ', and LF is a vertical angle with /D, what is the measure of ¿F?
Item 1
Item 2
COURSE TOOLS
(1 point)
O 48°
O 132°
O 31°
O 124°

Answer 1

To find the measure of angle LF, we need to determine the value of x first.

Since LD and LE are supplementary angles, their sum must be 180 degrees:
m/D + mLE = 180

Substituting the given values:
(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 know x = 31, we can find the measure of angle LF, which is a vertical angle with angle /D. Vertical angles are congruent, so the measure of angle LF is also (4x + 8) degrees:
mF = (4x + 8) = (4 * 31 + 8) = 124 degrees

Therefore, the measure of angle F is 124 degrees.