How to solve: the measure of an angle is 12 less than twice the measure of its supplement. What is the measure of the angle?
let the angle be x
then its supplement is 180-x
x = 2(180-x) - 12
x = 360 - 2x - 12
3x = 348
x = 116
check:
if the angle is 116
its supplement is 64
twice the supplement is 128
12 less than twice the supplement = 128-12 = 116
YEAH!
To solve this problem, follow these steps:
Step 1: Let's assume the measure of the angle is represented by 'x'.
Step 2: We know that the supplement of an angle is 180 degrees minus the angle itself. So, the measure of the supplement is (180 - x) degrees.
Step 3: According to the problem statement, the measure of the angle is 12 less than twice the measure of its supplement. In equation form, this can be written as:
x = 2(180 - x) - 12
Step 4: Simplify the equation:
x = 360 - 2x - 12
Step 5: Combine like terms:
x + 2x = 360 - 12
3x = 348
Step 6: Divide both sides of the equation by 3:
x = 116
Therefore, the measure of the angle is 116 degrees.
To solve this problem, we need to set up an equation.
Let's represent the measure of the angle as "x".
According to the problem, the angle is 12 less than twice the measure of its supplement. The supplement of an angle is the angle that, when added to the original angle, equals 180 degrees.
So, the measure of the angle's supplement is 180 - x.
Twice the measure of the angle's supplement is 2(180 - x), which is equal to 360 - 2x.
The problem states that the measure of the angle is 12 less than twice the measure of its supplement. We can set up the equation as follows:
x = 360 - 2x - 12
Now, we can solve for x by combining like terms and isolating x.
First, let's bring the x terms to one side:
x + 2x = 360 - 12
Combining like terms:
3x = 348
Then, divide both sides by 3:
x = 348/3
Simplifying:
x = 116
Therefore, the measure of the angle is 116 degrees.
x + (2x - 12) = 180
3x - 12 = 180
3x = 180
+ 12
____
3x =192
192/3= x