The Angle and Its Complement

To find the angle which is four times its complement, we first need to understand the concept of complementary angles. Complementary angles are two angles that add up to 90 degrees.

Definition: Two angles are said to be complementary if the sum of their measures is equal to 90 degrees.

Let's assume the angle we are looking for is 'x'. Its complement can be represented as (90 - x), as the sum of the angle and its complement is 90 degrees.

Step 1: Define the problem
We need to find the angle 'x' that is four times its complement.

Step 2: Set up an equation
According to the given information, we can set up the equation:
x = 4(90 - x)

Step 3: Solve the equation
Now, let's solve the equation to find the value of 'x':

x = 4(90 - x)
x = 360 - 4x
5x = 360
x = 72

Step 4: Verify the solution
To verify our solution, we need to check if the angle 'x' is indeed four times its complement:

Complement of x = 90 - x = 90 - 72 = 18
4 times the complement = 4 * 18 = 72

Since the angle 'x' is equal to four times its complement (72 = 4 * 18), our solution is correct.

Conclusion
The angle we were looking for is 72 degrees, and it is four times its complement. This means that the angle and its complement add up to 90 degrees, as expected.

x-4(90-x)x-360+4x5x =360 x=360÷5x=72