the measure of one angle is described as twelve more than four times a number. its supplement is twice as large. find the measure of each angle.
if the angle is x, its supplement is 180-x, so just solve
180-x = 2x
x=60
What's all this nonsense about x=4n+12?
If you need to find "the number" then just solve that for n, given that x=60.
The measure of one angle is described a number
To find the measure of each angle, we'll set up an equation based on the given information.
Let's assume the angle is represented by the variable 'x'. According to the information provided:
- The measure of one angle is described as twelve more than four times a number, which can be written as: 4x + 12.
- The supplement of the angle is twice as large, so the measure of the supplement can be written as: 2(4x + 12).
Now, we can set up an equation:
The angle + Its supplement = 180 degrees (since they are supplementary angles)
x + 2(4x + 12) = 180
Simplifying the equation:
x + 8x + 24 = 180
9x + 24 = 180
9x = 180 - 24
9x = 156
x = 156/9
x ≈ 17.33
So, the measure of the angle is approximately 17.33 degrees.
To find the measure of its supplement, we substitute the value of x into the expression:
Supplement = 2(4x + 12)
Supplement = 2(4*17.33 + 12)
Supplement ≈ 2(69.32 + 12)
Supplement ≈ 2(81.32)
Supplement ≈ 162.64
Therefore, the measure of the angle is approximately 17.33 degrees, and the measure of its supplement is approximately 162.64 degrees.