To find the measures of two complementary angles that are in the ratio of 1 to 5, we first need to understand what complementary angles are. Complementary angles are two angles whose sum is 90 degrees.
Let’s denote the smaller angle as x. Because the angles are in the ratio of 1 to 5, the larger angle can be expressed as 5x.
Now, since these angles are complementary, we can write the following equation:
x + 5x = 90
Combining like terms gives us:
6x = 90
Next, we solve for x by dividing both sides of the equation by 6:
x = 90 / 6
This simplifies to:
x = 15
Now that we have the value of x, we can find the measures of both angles:
- Smaller angle: 15 degrees
- Larger angle: 5x = 5 * 15 = 75 degrees
Therefore, the two complementary angles are 15 degrees and 75 degrees.