The measure of the supplement of an angle is 20 degrees more than three times the measure of the original angle. Find the measures of the angles.
Let x=original angle
180-x=20+3x
solve for x.
Let's assume the measure of the original angle is x degrees.
According to the problem statement, the measure of the supplement of the angle is 20 degrees more than three times the measure of the original angle. Therefore,
Supplement of the angle = 3x + 20
Now, we know that the sum of the measures of an angle and its supplement is 180 degrees. Therefore,
x + (3x + 20) = 180
Simplifying the equation:
4x + 20 = 180
Subtracting 20 from both sides of the equation:
4x = 160
Dividing both sides of the equation by 4:
x = 40
So, the measure of the original angle is 40 degrees.
Now, to find the measure of the supplement of the angle, we substitute the value of x back into the equation:
Supplement of the angle = 3x + 20
Supplement of the angle = 3(40) + 20
Supplement of the angle = 120 + 20
Supplement of the angle = 140
Therefore, the measure of the supplement of the angle is 140 degrees.
To summarize, the measures of the angles are:
Original angle = 40 degrees
Supplement of the angle = 140 degrees
To find the measures of the angles, let's first represent the original angle as x.
We know that the supplement of an angle is 180 degrees minus the angle itself. So, the supplement of the original angle is 180 - x degrees.
According to the problem, the measure of the supplement is 20 degrees more than three times the measure of the original angle. This can be written as:
180 - x = 3x + 20
Now, let's solve this equation to find the value of x.
First, simplify the equation:
180 = 4x + 20
Next, isolate the variable by subtracting 20 from both sides:
180 - 20 = 4x
160 = 4x
Finally, divide both sides by 4 to solve for x:
x = 160 / 4
x = 40
So, the original angle measures 40 degrees.
To find the measure of its supplement, substitute the value of x back into the equation:
Supplement angle = 180 - x = 180 - 40 = 140
Therefore, the measure of the supplement angle is 140 degrees.