Problem:
Find the angle which is four times its complement and is 10 degrees less than twice of its complement.

Solution:

Let's assume the angle we are looking for is represented by "x".

Step 1: Define Complement of an Angle

The complement of an angle is defined as the angle that, when added to the given angle, forms a right angle (90 degrees). In other words, the complement of an angle is the difference between 90 degrees and the given angle.

Step 2: Express the angle and its complement in terms of x

- The angle is x.
- The complement of the angle is 90 - x.

Step 3: Set up the equation

According to the problem statement, four times the complement of the angle is 10 degrees less than twice the complement of the angle. Mathematically, this can be expressed as:

4(90 - x) = 2(90 - x) - 10

Step 4: Solve the equation

Let's solve the equation step-by-step:

4(90 - x) = 2(90 - x) - 10
360 - 4x = 180 - 2x - 10
360 - 180 + 10 = -2x + 4x
190 = 2x
x = 190/2
x = 95

Step 5: Verify the solution

To verify the solution, we can substitute the value of x into the equation:

4(90 - 95) = 2(90 - 95) - 10
4(-5) = 2(-5) - 10
-20 = -10 - 10
-20 = -20

The equation holds true, which means the angle x = 95 degrees satisfies the given conditions.

Conclusion:
The angle we are looking for is 95 degrees.

4(90-x)+10=2(90-x)
360-4x+10 =180-2x
370-180=4x-2x
190=2x
95=x
Correct me if I'm wrong but I feel like your question has a little error in it