The measure of the supplement of an angle is one fourth the measure of the angle. What is the measure of each angle?
Supplementary angles: x + y = 180
From the problem, we can state that: y = (1/4)x
Substituting back to the first equation, we have:
x + (1/4)x = 180
(5/4)x = 180
x = ? (You can calculate this yourself)
As to find the supplementary angle, you can use the result for x by using the equation y = (1/4)x
To find the measure of each angle, let's first define the angle as 'x'.
According to the problem, the measure of the supplement of an angle (180 degrees minus the angle) is one fourth the measure of the angle.
So, the measure of the supplement of angle x is given by: (180 - x).
According to the problem, (180 - x) equals one fourth of x.
We can write this as an equation:
180 - x = 1/4 * x
To solve this equation, let's simplify:
Multiply both sides by 4 to eliminate the fraction:
4(180 - x) = x
Distribute the 4:
720 - 4x = x
Add 4x to both sides:
720 = 5x
Divide both sides by 5:
x = 720/5
Simplifying:
x = 144
So, the measure of each angle is 144 degrees.
Let's assume the measure of the angle is x.
According to the given information, the measure of the supplement of the angle is one fourth the measure of the angle.
The supplement of an angle is 180 degrees minus the angle itself.
So, the measure of the supplement of the angle is 180 - x.
Now, we can set up the equation:
180 - x = (1/4)x
To solve this equation, let's simplify it:
180 = (1/4)x + x
Multiply both sides of the equation by 4 to get rid of the fraction:
720 = x + 4x
Combine like terms:
720 = 5x
Divide both sides by 5:
144 = x
Therefore, the measure of the angle is 144 degrees.
To find the measure of the supplement of the angle, substitute the value of x into the equation for the supplement:
180 - x = 180 - 144 = 36 degrees
Therefore, the measure of the supplement of the angle is 36 degrees.