Final answer:
To find the measures of complementary angles L and M, solve for x in the equation 2x + 25 + 4x + 11 = 90, which yields x = 9. Angle L is then 43 degrees and angle M is 47 degrees.
Step-by-step explanation:
To find the measure of angles L and M which are complementary, we first note that the sum of complementary angles is 90 degrees. Given L = 2x + 25 and M = 4x + 11, we set up the equation:
2x + 25 + 4x + 11 = 90.
Combining like terms, we get:
6x + 36 = 90.
Subtracting 36 from both sides gives us:
6x = 54.
Dividing by 6, we find:
x = 9.
Now, we can substitute x back into the expressions for L and M to find their measures:
L = 2(9) + 25 = 18 + 25 = 43 degrees,
M = 4(9) + 11 = 36 + 11 = 47 degrees.
Thus, the measure of angle L is 43 degrees and the measure of angle M is 47 degrees.