An angle is 30 less than half its complement. Find the angle.

Why did the angle go to therapy? Because it couldn't handle being half the person its complement was! Now, let's solve this little riddle together.

Let's call the angle "A" and its complement "C". According to the given information, we can express the relationship between the angle and its complement as:

A = (1/2)C - 30

But we also know that the sum of an angle and its complement is 90 degrees. So we have the equation:

A + C = 90

Now, let's substitute the value of A from the first equation into the second equation:

(1/2)C - 30 + C = 90

Combining like terms, we have:

(3/2)C - 30 = 90

Adding 30 to both sides of the equation, we get:

(3/2)C = 120

Dividing both sides by (3/2), we find:

C = 80

So the complement of the angle is 80 degrees. Now, let's plug this value back into the first equation to find the angle:

A = (1/2)(80) - 30

A = 40 - 30

A = 10

Voila! The angle is 10 degrees.

Let's denote the angle as x.

The complement of the angle is equal to 90 degrees minus the angle. So the complement of the angle is (90 - x) degrees.

According to the given information, the angle is 30 degrees less than half its complement. This can be expressed as:

x = (1/2)(90 - x) - 30

Now, let's solve the equation:

x = (1/2)(90 - x) - 30

Multiplying both sides of the equation by 2 to eliminate the fraction:

2x = 90 - x - 60

Combining like terms:

2x + x = 90 - 60

3x = 30

Dividing both sides of the equation by 3 to solve for x:

x = 10

Therefore, the angle is 10 degrees.

To find the angle, let's first define the given information.

Let the angle be denoted as "x."
The complement of an angle is the angle that, when added to the given angle, equals 90 degrees. The complement of x is represented as "90 - x."
Given that the angle is 30 less than half its complement, we can write the equation:

x = (1/2)(90 - x) - 30

To solve for x, follow these steps:

Step 1: Distribute (1/2) to (90 - x).

x = (1/2)(90) - (1/2)(x) - 30

Step 2: Simplify the equation.

x = 45 - (x/2) - 30

Step 3: Combine like terms.

x = 15 - (x/2)

Step 4: To get rid of the fraction, multiply both sides by 2.

2x = 30 - x

Step 5: Add x to both sides.

2x + x = 30

Step 6: Combine like terms.

3x = 30

Step 7: Divide both sides by 3 to solve for x.

x = 10

Therefore, the angle is 10 degrees.

x = (90-x)/2 - 30