use the triangle sum theorem to find the largest angle in a triangle with angle measures of (x - 20)° , (3x + 3)°, and (2x - 7)°.
The sum of the angles in a triangle is always 180° according to the triangle sum theorem. Therefore, we have:
(x - 20) + (3x + 3) + (2x - 7) = 180
6x - 24 = 180
6x = 204
x = 34
Now we can find the measures of the angles:
1st angle: (x - 20)° = (34 - 20)° = 14°
2nd angle: (3x + 3)° = (3*34 + 3)° = 105°
3rd angle: (2x - 7)° = (2*34 - 7)° = 61°
Therefore, the largest angle in the triangle is 105°.