Final answer:
Two complementary angles are related by the equation 2x = 3y and their sum is 90 degrees. By solving this system of equations, we find that the larger angle is 54 degrees.
Step-by-step explanation:
To solve this problem, we can set up an equation using the given information. Let's call one angle x and the other angle y. We are told that two times x is equal to three times y. This can be written as 2x = 3y. We also know that the sum of the two angles is 90 degrees, since they are complementary. So, we have x + y = 90.
We can solve this system of equations by substitution or elimination. Let's use substitution.
We can rearrange the first equation to solve for y: y = (2/3)x.
Substitute this into the second equation: x + (2/3)x = 90.
Combine like terms: (5/3)x = 90. Divide both sides by (5/3) to solve for x: x = (3/5)*90 = 54 degrees.
So, the larger angle is x, which is 54 degrees.
Therefore, the answer is D. 54 degrees.
Learn more about Complementary angles