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 measures of the angles in a triangle is 180 degrees.
So, we have the equation: (x-20) + (3x+3) + (2x-7) = 180.
Combining like terms: 6x - 24 = 180.
Adding 24 to both sides: 6x = 204.
Dividing both sides by 6: x = 34.
Now we can substitute this value of x back into each angle measure to find their respective values:
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.