An angle is 15 less than four times its supplement. Find both angle measures.

A = X Deg.

B = (4x-15) Deg.

A + B = 180o.
X + (4x-15) = 180
X + 4x - 15 = 180
5x = 180 + 15 = 195

X = 39o
4x - 15 = 4*39 - 15 = 141o.

Well, well, well, we have a classic math problem here! Let's call the angle "x" (because angles like to keep things mysterious) and its supplement "y" (they do say opposites attract).

According to the question, we have two clues. First, the angle is 15 less than four times its supplement. So, we can write this as an equation: x = 4y - 15.

But wait, there's more! We also know that supplementary angles add up to 180 degrees (because angles have a knack for keeping things fair and balanced). So, we can write another equation: x + y = 180.

Now, it's time to take these equations for a spin on the dancefloor of mathematics. Let's solve the equations simultaneously to find our angle measures.

Substituting the value of x from the first equation into the second equation, we get (4y - 15) + y = 180.

Combining like terms, we have 5y - 15 = 180.

Adding 15 to both sides, we have 5y = 195.

Dividing both sides by 5, we find y = 39.

Now that we know y, we can substitute this value back into the first equation: x = 4(39) - 15.

Calculating this, we find x = 141.

So, our angle measures are x = 141 degrees and y = 39 degrees. 141 and 39, like two peas in a mathematical pod!

Let's solve this step-by-step.

Step 1: Let's represent the angle by the variable "x"

Step 2: According to the problem statement, the angle is 15 less than four times its supplement.

Formula for the supplement of an angle is: 180 - x

So, we can write the equation as:

x = 4(180 - x) - 15

Step 3: Simplify the equation.

x = 720 - 4x - 15

We can simplify this to:

x + 4x = 720 - 15

5x = 705

Step 4: Solve for x

Divide both sides of the equation by 5:

x = 705/5

x = 141

So, the angle measures 141 degrees.

Step 5: Find the supplement of the angle.

The supplement of an angle is 180 degrees minus the angle.

Supplement = 180 - x = 180 - 141 = 39

So, the supplement of the angle measures 39 degrees.

In conclusion, the angle measures 141 degrees, and its supplement measures 39 degrees.

To find the angle measures, we need to set up an equation based on the information given.

Let's assume the angle is represented by "x" and its supplement (the other angle that adds up to 180 degrees) is represented by "y".

According to the given information, we can set up the equation:

x = 4y - 15

We also know that the sum of two supplementary angles is 180 degrees:

x + y = 180

Now we can solve the system of equations to find the values of x and y.

Substituting the first equation into the second equation:

4y - 15 + y = 180

Combining like terms:

5y - 15 = 180

Adding 15 to both sides:

5y = 195

Dividing both sides by 5:

y = 39

Now substitute this value back into the first equation to find x:

x = 4 * 39 - 15
x = 156 - 15
x = 141

So, the angle measures are x = 141 degrees and y = 39 degrees.