One angle of a triangle is 2 more than four times as large as the other angle. The third angle is three times the first angle decreased by 6. What is the measure of each angle?
x+4x+2+3x-6=180
7x=180+6-2
7x=184
x=26.3
angle 1: 23.3, Angle 2: 107.1, and angle 3: 71.9
Are the angles correct?
You should define your variables, hard to check without knowing what x stands for
e.g.
let the "other " angle be x
then "one" angle is 4x+2
"The third angle is three times the first angle decreased by 6" ---> poor wording.
How do we know which is the "first" angle ?
the third angle could be either 3x - 6
or
3(4x+2) - 6 = 12x
case 1:
x + 4x+2 + 3x-6 = 180
8x = 184
x = 23
the angles are 23° , 94, and 63°
case 2:
x + 4x+2 + 12x = 180
17x = 180
x = 180/17
etc.
probably my first interpretation
your error is the 7x, should have been 8x
To find the measure of each angle in the triangle, we can set up an equation using the given information and solve for the variables.
Let the measure of the first angle be x.
According to the problem, the second angle is 2 more than four times the first angle. Therefore, the measure of the second angle is 4x + 2.
The third angle is three times the first angle decreased by 6. So, the measure of the third angle is 3x - 6.
We know that the sum of all angles in a triangle is 180 degrees. Therefore, we can set up the equation:
x + (4x + 2) + (3x - 6) = 180.
Now, let's solve this equation to get the value of x.
Combining like terms, we have:
8x - 4 = 180.
Adding 4 to both sides, we get:
8x = 184.
Dividing both sides by 8, we find:
x = 23.
Now that we have the value of x, we can substitute it back into the expressions for the second and third angles to find their measures:
The second angle is 4x + 2 = 4(23) + 2 = 92 + 2 = 94.
The third angle is 3x - 6 = 3(23) - 6 = 69 - 6 = 63.
Therefore, the measures of the angles are:
Angle 1: x = 23.
Angle 2: 4x + 2 = 94.
Angle 3: 3x - 6 = 63.
So, the angles are calculated as Angle 1: 23°, Angle 2: 94°, and Angle 3: 63°.