Question

Two angles are complementary if the sum of their measures is 90° Find two complementary angles such that the smaller angle is 206° less than 3 times the larger angle. (Round to two decimal places if necessary.)

Answer 1

To find two complementary angles, we can set up two equations based on the given information and solve them to find the values of the angles.

Step-by-step explanation:

To solve this problem, we need to set up an equation based on the information given. Let's assume that the larger angle is x degrees. According to the problem, the smaller angle is 206° less than 3 times the larger angle. So the equation we can form is: 3x - 206° = the smaller angle.

Since we know that two angles are complementary if their sum is 90°, we can write another equation based on this: x + the smaller angle = 90°.

Now, we can use these equations to find the values of the two angles. First, solve the first equation for the smaller angle and substitute it in the second equation. Then solve for x, and finally substitute that value back to find the smaller angle. Round to two decimal places if necessary.