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) ° .
According to the triangle angle sum theorem, the sum of the three angles in any triangle is 180 degrees. Therefore, we can write the equation as follows:
(x - 20) + (3x + 3) + (2x - 7) = 180
Simplifying the equation, we get:
6x - 24 = 180
Adding 24 to both sides of the equation:
6x = 204
Dividing both sides by 6:
x = 34
Now, we can substitute this value of x into the angle measures:
Angle 1: (x - 20) = (34 - 20) = 14 degrees
Angle 2: (3x + 3) = (3 * 34 + 3) = 105 degrees
Angle 3: (2x - 7) = (2 * 34 - 7) = 61 degrees
Therefore, the largest angle in the triangle is 105 degrees.