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) °
The Triangle Angle Sum Theorem states that the sum of the measures of the interior angles of a triangle is always 180°.
So, we can set up an 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 find the measures of each angle:
Angle 1: (x - 20) = (34 - 20) = 14°
Angle 2: (3x + 3) = (3(34) + 3) = 105°
Angle 3: (2x - 7) = (2(34) - 7) = 61°
Therefore, the largest angle in the triangle is 105°.