If three time the supplement of an < is subtracted from seven times the comp. of the <, the answer is the same at that obtained by trisecting a right <. Find the supplement.
(I tried to set it up this way, but it didn't work. What did I do wrong???)
3(180-x) - 7(90-x)= 30
In order to solve this problem, let's break it down step by step:
Step 1: Understand the problem
We are given that three times the supplement of an angle is subtracted from seven times the complement of the angle, and the result is equal to the angle obtained by trisecting a right angle. We need to find the supplement of the angle.
Step 2: Define the variables
Let's assume the angle we are looking for is "x".
Step 3: Express the given information as equations
We know that three times the supplement of an angle is subtracted from seven times the complement of the angle. The complement of an angle is found by subtracting the angle from 90 degrees, and the supplement is found by subtracting the angle from 180 degrees. So we can write the equation as:
7(90 - x) - 3(180 - x) = 30
Step 4: Solve the equation
Let's simplify and solve the equation:
630 - 7x - 540 + 3x = 30
90 - 4x = 30
-4x = 30 - 90
-4x = -60
x = -60 / -4
x = 15
Step 5: Find the supplement of the angle
The supplement of an angle is found by subtracting the angle from 180 degrees. So the supplement of angle x is:
180 - 15 = 165
Therefore, the supplement of the angle is 165 degrees.
To solve this problem, let's analyze the equation you set up and see what went wrong.
You started by defining the supplement of an angle as 180 minus the angle: 180 - x. Similarly, you defined the complement of an angle as 90 minus the angle: 90 - x. Then you set up the equation as follows:
3(180 - x) - 7(90 - x) = 30
Let's simplify this equation step by step:
3(180 - x) - 7(90 - x)
First, let's apply the distributive property:
= 540 - 3x - 630 + 7x
Now combine like terms:
= -90 + 4x
The equation becomes:
-90 + 4x = 30
To solve for x, isolate the variable term:
4x = 30 + 90
4x = 120
x = 120/4
x = 30
So, according to your equation, the value of x, which represents the angle, would be 30 degrees. However, we want to find the supplement of the angle.
The supplement of an angle is 180 degrees minus the angle itself. Thus, the supplement of the angle would be:
180 - x = 180 - 30 = 150 degrees
So the supplement of the angle is 150 degrees.
It seems like you made a mistake in your set-up by using the complement instead of the supplement of the angle. Remember, the complement is 90 degrees minus the angle, while the supplement is 180 degrees minus the angle.