The measure of one angle is 7 times the measure of its complement. What is the measure of each angle?
To solve this problem, we need to understand what a complement of an angle is. Two angles are said to be complements of each other if their sum is 90 degrees.
Let's assume that the first angle is represented by "x" degrees. Since we are told that this angle is 7 times the measure of its complement, we can express the second angle as 7x degrees.
According to the definition of complementary angles, the sum of these two angles should be 90 degrees:
x + 7x = 90
Simplifying the equation, we combine like terms:
8x = 90
Next, we can solve for x by dividing both sides of the equation by 8:
x = 90 / 8
x = 11.25
Now that we have the value of x, we can find the measure of each angle by substituting it back into the expressions we derived earlier:
First angle: x = 11.25 degrees
Second angle: 7x = 7(11.25) = 78.75 degrees
Therefore, the measure of the first angle is 11.25 degrees, and the measure of the second angle is 78.75 degrees.