Use the triangle angle sum theorem to find the largest angle in a triangle with angle measures of (x-20) *, (3x+3) *, and (2x-7) * . (1 point)
According to the triangle angle sum theorem, the sum of the measures of the angles in a triangle is always 180 degrees.
So, we can write the equation:
(x-20) + (3x+3) + (2x-7) = 180
Simplifying the equation:
x - 20 + 3x + 3 + 2x - 7 = 180
Combine like terms:
6x - 24 = 180
Add 24 to both sides:
6x = 204
Divide by 6:
x = 34
Now we can substitute the value of x back into the angle measures:
First angle = x - 20 = 34 - 20 = 14 degrees
Second angle = 3x + 3 = 3(34) + 3 = 105 degrees
Third angle = 2x - 7 = 2(34) - 7 = 61 degrees
Therefore, the largest angle is 105 degrees.