A triangle is such that the largest angle is 12 times the smallest angle. The third angle is 20 less than the largest angle. Find the measure of each angle. (12-x)+ x+20-(12-x)=180.
im having a difficult time setting up the equation
what's with the 12-x? "12 times" means 12*
x + 12x + 12x-20 = 180
You seem to have a problem distinguishing between subtraction and multiplication.
To set up the equation, let's assign variables to the angles in the triangle.
Let's call the smallest angle x.
According to the given information, the largest angle is 12 times the smallest angle. So the largest angle would be 12x.
The third angle is 20 less than the largest angle. Therefore, the third angle would be (12x - 20).
Now we know the sum of the angles in a triangle is always 180 degrees. So we can set up the equation as follows:
x + 12x + (12x - 20) = 180
Simplifying the equation, we have:
25x - 20 = 180
To isolate x, we can add 20 to both sides of the equation:
25x = 200
Finally, dividing both sides by 25 gives us:
x = 8
Now we can substitute the value of x back into the original equation to find the measures of the other angles.
The smallest angle is x = 8 degrees.
The largest angle is 12x = 12 * 8 = 96 degrees.
The third angle is 12x - 20 = 12 * 8 - 20 = 96 - 20 = 76 degrees.
Therefore, the measures of the angles are 8 degrees, 96 degrees, and 76 degrees.