Final answer:
To find the measures of the complementary angles L and M, we solve the equation 2x + 25 + 4x + 11 = 90 to find x, and then substitute x back into the expressions for the angles. Angle L is 43 degrees, and angle M is 47 degrees.
Step-by-step explanation:
The student is asking about finding the measure of two angles that are complementary. The expressions for the angle measures are m∠L = 2x + 25 and m∠M = 4x + 11. Since the angles are complementary, their measures must add up to 90 degrees. We can set up the equation:
2x + 25 + 4x + 11 = 90
To find the value of x, we combine like terms and solve the equation:
6x + 36 = 90
6x = 54
x = 9
Now, we can find the measure of each angle by substituting x = 9 back into the original expressions:
- Degree Measure of angle L: m∠L = 2(9) + 25 = 18 + 25 = 43 degrees
- Degree Measure of angle M: m∠M = 4(9) + 11 = 36 + 11 = 47 degrees
Angle L measures 43 degrees and angle M measures 47 degrees, and they add up to 90 degrees, confirming that they are indeed complementary.