The Angle which is Five Times its Complement

An angle and its complement are two angles that add up to 90 degrees. Let's assume the measure of the angle is x degrees. The complement of this angle can be found by subtracting the measure of the angle from 90 degrees, which gives us 90 - x degrees.

Now, we are given that the angle is five times its complement. Mathematically, this can be expressed as:

x = 5(90 - x)

To solve this equation, we can distribute the 5 on the right side:

x = 450 - 5x

Next, we can add 5x to both sides of the equation to isolate the x term:

6x = 450

Dividing both sides of the equation by 6, we find:

x = 75

Therefore, the measure of the angle is 75 degrees.

Summary:
- An angle and its complement add up to 90 degrees.
- Let's assume the measure of the angle is x degrees.
- The complement of the angle can be found by subtracting the measure of the angle from 90 degrees: 90 - x degrees.
- We are given that the angle is five times its complement, so we can set up the equation: x = 5(90 - x).
- Simplifying the equation, we get: x = 450 - 5x.
- By isolating the x term, we add 5x to both sides: 6x = 450.
- Dividing both sides by 6, we find that x = 75.
- Therefore, the measure of the angle is 75 degrees.

The angle which is five times its complement is 75 degree