To find the measures of the two complementary angles that are in the ratio of 1 to 5, we can start by defining the angles in terms of a variable. Let’s say the first angle is represented by x. Since the angles are in the ratio of 1 to 5, we can express the second angle as 5x.
Complementary angles are two angles that add up to 90 degrees. Therefore, we can set up the equation:
x + 5x = 90
This simplifies to:
6x = 90
Now, we can solve for x by dividing both sides by 6:
x = 15
Now that we have the measure of the first angle (15 degrees), we can find the measure of the second angle by substituting x back into the expression for the second angle:
5x = 5(15) = 75 degrees
Therefore, the two complementary angles are:
- First angle: 15 degrees
- Second angle: 75 degrees