Findd the numerical measures of the angles whose measures are:
x, 3x-10, and 3(55-x)
If these are the angles of a triangle, they add to 180, so
x + 3x-10 + 3(55-x) = 180
x + 3x - 10 + 165 - 3x = 180
x = 25
So the angles are
25, 65, 90
To find the numerical measures of the angles, we need to set up an equation and solve for x.
Given that the measures of the angles are x, 3x-10, and 3(55-x), we can set up the equation:
x + 3x-10 + 3(55-x) = 180
Simplifying the equation:
x + 3x - 10 + 165 - 3x = 180
Combining like terms:
x + 3x - 3x - 10 + 165 = 180
2x + 155 = 180
Subtracting 155 from both sides:
2x = 25
Dividing both sides by 2:
x = 12.5
Now that we have found the value of x, we can plug it back into the equation to find the numerical measures of the angles.
The first angle:
x = 12.5
The second angle:
3x - 10 = 3(12.5) - 10 = 37.5 - 10 = 27.5
The third angle:
3(55 - x) = 3(55 - 12.5) = 3(42.5) = 127.5
Therefore, the numerical measures of the angles are:
First angle: 12.5 degrees
Second angle: 27.5 degrees
Third angle: 127.5 degrees