Two complementary angles are such that two times the measure of one is equal to three times the measure of the other. Which of the following is the measure of the larger angle? A. 72° B. 108° C. 36° D. 54°

Let's call the measure of the smaller angle x degrees. According to the problem, two times the measure of one angle (2x) is equal to three times the measure of the other angle (3x) because they are complementary angles.

So, we can write the equation:
2x = 3x

Now, we can solve for x by subtracting 2x from both sides of the equation:
2x - 2x = 3x - 2x
0 = x

Now that we know the measure of the smaller angle is x = 0 degrees, we can find the measure of the larger angle by using the fact that the sum of complementary angles is 90 degrees.

Larger angle = 90 degrees - Smaller angle = 90 degrees - 0 degrees = 90 degrees

So, the measure of the larger angle is 90 degrees. None of the options provided match this result. It's possible that there might be an error in the options given, or there may be some additional information missing from the problem statement.