The measure of an angle is twenty more than three times it's supplement. What are the measures of each angle?
Let x = the smaller angle.
x + 3x + 20 = 180
x = 20+3(180-x)
To find the measures of the angles, let's set up an equation.
Let's assume the measure of the angle is x. Since we are given that the measure of an angle is twenty more than three times its supplement, we can write the equation as:
x = 3(180 - x) + 20
First, we need to remember that supplementary angles add up to 180 degrees. So, the supplement of an angle can be found by subtracting the measure of the angle from 180.
Now, let's solve the equation:
x = 3(180 - x) + 20
Distribute the 3 on the right side of the equation:
x = 540 - 3x + 20
Combine like terms:
x + 3x = 540 + 20
4x = 560
Divide both sides of the equation by 4 to isolate x:
4x/4 = 560/4
x = 140
So, the measure of the angle is 140 degrees.
Now, to find the measure of its supplement, we can subtract the angle's measure from 180:
180 - x = 180 - 140 = 40
So, the measure of the supplement angle is 40 degrees.
Therefore, the measures of the angles are 140 degrees and 40 degrees.