Find the measure of an angle if its measure is 8 less than its complement
x + x - 9 = 90
x + x - 8 = 90
To find the measure of an angle if it is 8 less than its complement, we first need to understand what the complement of an angle means.
The complement of an angle is the angle that, when added to the given angle, forms a right angle (which measures 90 degrees). In other words, the sum of an angle and its complement is equal to 90 degrees.
Let's assume the measure of the given angle is "x". According to the problem, this angle is 8 less than its complement. Mathematically, we can represent this as:
x = (complement of x) - 8
Using the concept of angle complements, we know that the sum of an angle and its complement is equal to 90 degrees. Therefore, we can express the complement of the given angle as (90 - x).
Now we can substitute this value into our equation:
x = (90 - x) - 8
Next, let's solve for x:
x = 90 - x - 8
Combine like terms:
2x = 90 - 8
2x = 82
Divide both sides of the equation by 2:
x = 82 / 2
x = 41
Therefore, the measure of the angle is 41 degrees.