The measure of the complement of an angle is equal to 1/5 of the measure of its supplement. Find the measure of this angle.
90º - a = (180º - a) / 5
450 - 5a = 180 - a
270 = 4a
To solve this problem, let's first understand the definitions of complement and supplement.
Complement: The complement of an angle is the angle that, when added to the given angle, equals 90 degrees.
Supplement: The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees.
Let's say the measure of the given angle is x.
According to the given information, the measure of its complement is equal to 1/5 of its supplement.
We can set up the following equation to represent this relationship:
Complement = 1/5 * Supplement
Since complement + angle = 90 and supplement + angle = 180, we can write the following equations:
x + Complement = 90
x + Supplement = 180
Now we can substitute the values with the given information into these equations.
x + (1/5 * Supplement) = 90
x + Supplement = 180
To solve for x, we need to eliminate the variable "Supplement" from the equations. We can do this by multiplying the first equation by 5 to eliminate the fraction:
5 * (x + (1/5 * Supplement)) = 5 * 90
5x + Supplement = 450
Next, we can subtract the second equation from the first equation to eliminate the variable x:
(5x + Supplement) - (x + Supplement) = 450 - 180
4x = 270
Divide both sides of the equation by 4:
4x/4 = 270/4
x = 67.5
Therefore, the measure of the angle is 67.5 degrees.