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ZL and ZM are complementary, mZL = 2x + 25, and mZM = 4x + 11. Determine the measure of each angle.

(a) Degree Measure of angle L is 2x + 25
(b) Degree Measure of angle M is 4x + 11

1 Answer

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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.

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