Two angles are complementary if the sum of their measures is $90^{\circ}$. Find two complementary angles such that one of the angles is $218^{*}$ less than 3 times the other angle. (Round to two decimal places if necessary.) Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts - the smaller complementary angle - the larger complementary angle

Step 1 ：Let's denote the smaller angle as x and the larger angle as y.

Step 2 ：We have two equations based on the problem: \(x + y = 90\) (since the angles are complementary) and \(y = 3x - 218\) (since one angle is 218 degrees less than 3 times the other).

Step 3 ：Solving this system of equations, we find that x = 77 and y = 13.

Step 4 ：This means that the smaller angle is 77 degrees and the larger angle is 13 degrees.

Step 5 ：These two angles are complementary since their sum is 90 degrees, and the larger angle is 218 degrees less than 3 times the smaller angle.

Step 6 ：Final Answer: The smaller complementary angle is \(\boxed{77}\) degrees and the larger complementary angle is \(\boxed{13}\) degrees.