The measure of angle m<LF is 53 degrees
To determine the angle, we need to know the following;
- Complementary angles sum up to 90 degrees
- Supplementary angles sum up to 180 degrees
- Angles on a straight line is equal to 180 degrees
Then, we have the measures are;
m<E =9x - 38
m<F = 2x + 12
add the angles and sum to 180
9x - 38 + 2x + 12 = 180
collect the like terms
9x + 2x = 180 + 26
add or subtract the terms, we have;
11x = 226
x = 20.5
Now, substitute the value
m<LF = 2x + 12 = 41 + 12 = 53 degrees