The supplement of an angle is 12 less than 4 times the complement of the angle. What is the measure of the angle?
Well, I guess this angle really needs to work on its social skills. It's all about making friends with complements and supplements in the geometry world. Let's see if we can solve this equation.
Let's call the measure of the angle 'x'. The supplement of the angle is 180 - x degrees, and the complement of the angle is 90 - x degrees.
According to the information given, the supplement of the angle is 12 less than 4 times the complement of the angle. In equation form, this can be written as:
180 - x = 4(90 - x) - 12
Now, let's simplify and solve for x:
180 - x = 360 - 4x - 12
180 + 12 = 360 - 4x + x
192 = 360 - 3x
3x = 360 - 192
3x = 168
x = 168/3
x = 56
So, the measure of the angle is 56 degrees. Now, go out there and make friends with complements and supplements!
To solve this problem, let's break it down step by step.
Step 1: Understand the problem.
We are given that the supplement of an angle is 12 less than 4 times the complement of the angle. We need to find the measure of the angle.
Step 2: Define the variables.
Let's define the angle as x.
Step 3: Understand the definitions.
The supplement of an angle is the angle that, when added to the given angle, forms a straight line, which measures 180 degrees.
The complement of an angle is the angle that, when added to the given angle, forms a right angle, which measures 90 degrees.
Step 4: Set up the equation.
We are given that the supplement of the angle (180 - x) is 12 less than 4 times the complement of the angle (4*(90 - x)). So, we can set up the equation as follows:
180 - x = 4*(90 - x) - 12
Step 5: Solve the equation.
Let's simplify and solve the equation.
180 - x = 360 - 4x - 12
Combine like terms:
180 - x = 348 - 4x
Add 4x to both sides:
4x + 180 - x = 348 - 4x + 4x
3x + 180 = 348
Subtract 180 from both sides:
3x + 180 - 180 = 348 - 180
3x = 168
Divide both sides by 3:
3x/3 = 168/3
x = 56
Step 6: Check the solution.
To check if our answer is correct, let's substitute the value of x into the original equation:
180 - x = 4*(90 - x) - 12
180 - 56 = 4*(90 - 56) - 12
124 = 4*(34) - 12
124 = 136 - 12
124 = 124
Since both sides of the equation are equal, we have verified that the angle is indeed 56 degrees.
So, the measure of the angle is 56 degrees.
angle --- x
complement = 90-x
supplement = 180-x
180-x = 4(90-x) - 12
solve for x