If there are two supplementary angles, LD and LE, where mLD = (4x + 8) ° and mLE = (x + 17) °
, and LF is a vertical angle with LD, what is the measure of LF?
Since LD and LE are supplementary, their measures sum up to 180 degrees. So we have the equation:
mLD + mLE = 180
(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, we can find the measure of LD:
mLD = (4x + 8) °
mLD = (4 * 31 + 8) °
mLD = (124 + 8) °
mLD = 132 °
Since LF is a vertical angle with LD, they have the same measure. Therefore, the measure of LF is also 132 degrees.